Book Description
“Current fans and recovering Hulkamaniacs alike should find [Sex, Lies, and Headlocks] as gripping as the Camel Clutch.” —Maxim
Sex, Lies, and Headlocks is the ultimate behind-the-scenes look at the backstabbing, scandals, and high-stakes gambles that have made wrestling an enduring television phenomenon. The man behind it all is Vince McMahon, a ruthless and entertaining visionary whose professional antics make some of the flamboyant characters in the ring look tame by comparison. Throughout the book, the authors trace McMahon’s rise to power and examine the appeal of the industry’s biggest stars—including Ed “Strangler” Lewis, Gorgeous George, Bruno Sammartino, Ric Flair, and, most recently, Stone Cold Steve Austin and The Rock. In doing so, they show us that while WWE stock is traded to the public on Wall Street, wrestling remains a shadowy world guided by a century-old code that stresses secrecy and loyalty.
With a new afterword, this is the definitive book about the history of pro wrestling.
“Reading this excellent behind-the-scenes look at wrestling promoter McMahon . . . is almost as entertaining and shocking as watching the most extreme antics of McMahon’s comic-book style creations such as Steve Austin and The Rock.”
—Publishers Weekly
“A quintessentially American success story of a cocky opportunist defying the odds and hitting it big . . . Sparkling cultural history from an author wise enough to let the facts and personalities speak for themselves.”—Kirkus Reviews
Customer Reviews:
The story of the Wrestling Bill Gates.......2007-07-23
An extremely interesting book, where you'll understand why Vince Mcmahon is wrestling Bill Gates, from its beginning until today, see all the tragedy that WWE has gone through, see all the backstage scheming which is a lot but interesting, Owen Hart death, Montreal Incident ( Bret Hart goes to WCW), Steroid Trial, Anabolic Jim ( Ultimate Warrior ), nobody can miss this book, its excellent.
A Somewhat Thorough, But Lacking Treatment.......2006-09-23
Written at the tail-end of the last great wrestling boom, this book's audience is ostensibly more of a mark-ish, or at the very least, naive group to the goings-on in the world of professional wrestling. The book itself is interesting, and moves at a fast pace, but often it moves too fast for its own good. Previous reviewers have mentioned that the last chapter feels cobbled together. I agree. It seems as though it was produced under deadline circumstances, and the clarity of the earlier portion of the book, which had been a strength, becomes a liability. Furthermore, the writers themselves lack credibility, as they write in a biased (although not readily obvious) tone. McMahon is treated as Satan incarnate, and that's their prerogative, which is perfectly acceptable. However, many of the workers within the business are treated with an unfair hand, and I think that has a lot to do with the way that the information was compiled in this book's research. One of the main subjects for interview for this piece was Kevin Nash. The problem that stems from Nash's presence isn't so much his own fault as it is that the authors clearly give him and those close to him the benefit of the doubt in many contentious issues, and the result is an unfair read to many in the business.
Nash's membership in the Kliq is widely known, and if one goes into the book knowing of it, certain tendencies arise. Shawn Michaels is essentially given a pass for the Montreal Screwjob, and most references to him in the book paint him as a hard worker and the soul of McMahon's company through the lean years. While the authors are entitled to such an opinion, it is clear that it is one heavily influenced my their own soft spot towards Nash. Hart is characterized as a sullen and thankless character, and the authors make explicit mentioning of his refusal to job to Michaels in Canada. What the authors don't mention is that Hart agreed to job to anyone else anywhere, even the infamous Brooklyn Brawler. Furthermore, they also disregard the fact that Hart's refusal to lay down for Michaels stems directly from Michaels' own admission that he wouldn't job to anyone in the company. Wrestlers like Rick Rude (who left the WWF acrimoniously after the Screwjob and delivered a searing promo on Michaels shortly thereafter) are vilified for their addiction to steroids presented as "old hags", but Nash friends Scott Hall and Sean Waltman are given the benefit of the doubt with their own substance abuse either avoided entirely (Waltman) or excused as the result of the wrestling lifestyle and personality disorders (Hall). Further Nash enemies such as Hulk Hogan are derided throughout the entire text for their political input on wrestling, with little mention of the political leverage (albeit somewhat nascent at this time) excerted by former Kliq member HHH.
Finally, the MSG incident is portrayed as a touching moment in the history of wrestling, rather than a serious breach of kayfabe that undermined the legitimacy of the WWF's product. This is in no small way furher evidence of inherent bias by the authors.
This may seem like the ranting of a Hart fan, but in reality, it's a more complete view of one picture that the authors could have painted better for the reader had they done more research, and not let their predilections for individuals take precedence over what is presented as a historical account of the WWF/E
A book that needed to be written.......2005-12-29
I feel that this is a book that needed to be written. Are the writers elitists who hate pro wrestling? That's not the point. The point, is that these guys are exposing the seedy underbelly of the sport. Don't get me wrong. I'm a wrestling fan and I've been watching the WWF/E since 1987. I've been a wrestling fan for 18 years now and that's not going to change; but I think it's a good thing that these guys are exposing the underhanded dealings that go on in the locker rooms and in the offices of WWE wrestlers and management.
Wrestlers have to be "according to Vince McMahon's philosophy, "bigger than life". To do this, they need characters the fans can relate to, but they also need *size* and for some of these wrestlers, the only way they can get bigger is to use steroids. Plus, while wrestling is predetermined and scripted, the moves done are real and carry real risk. Wrestlers have had bones broken and been paralyzed by falling wrong or taking too hard a hit. They ache after their matches and need to take pain pills to calm down their ravaged bodies. They also need pills to sleep and wake up. Not only that but they are on the road 200+ days a year traveling from city to city, forced to pay the majority of their travel and living expenses (hotel rooms, food, insurance, etc). Wrestlers have no union, no benefits, no guarantee of employment, and now that WCW and ECW are gone, no other options for employment (except for TNA but even then, the salaries of the wrestlers drop substantially). People need to be aware of just how much these people are sacrificing to entertain us. More needs to be done to prevent wrestlers from dying of drug overdoses, steroid abuse, or poor working conditions. Rick Rude, Road Warrior Hawk, Eddie Guerrero, Chris Candido, Owen Hart, and Brian Pillman are just some of the casualties of the business and the Monday Night War between WWF and WCW. If more people are aware of wrestling's seedy underbelly, perhaps someone will take action to make the business safer for all involved.
In addition, I was glad to read the book because, even with the mistakes, it provided a long term perspective on how the business has evolved since the formation of the National Wrestling Alliance and the territory system (something that I wasn't even aware of back in 1987 because my wrestling viewership was limited to WWF, and they had pretty much replaced the NWA as the nation's leading wrestling company by then). I would especially recommend the book to newer fans who probably wouldn't understand that in the 80's, wrestling didn't have huge firework displays before every Monday night show, nor huge/elaborate stages, nor the entrance video packages featuring the wrestlers.
The business has come a long way, but it still needs to evolve for the sake of everyone participating. I think that's the central theme of the book, and one that wrestling fans would be wise to learn about.
The Battles Outside the Ring.......2005-11-18
Here's a book that looks into wrestling itself. This is about some of the behind the scenes events that shaped or transformed wrestling into its current state, many of them being the tribulations and accusations faced by Vince McMahon and the WWWF/WWF/WWE. There is also ample coverage of the NWA/WCW presented here also. We travel towards the beginnings of the wrestling industry in the small arenas, barns, and fairgrounds of the 1920s up to roughly 2002 of big events, PPVs, and showmanship of today.
The book covers topics like Vince's buy out of his father, the territorial monopolization McMahon sets forth to conquer the wrestling world, the rise of wrestling on TV, egotistical stars rising and falling, the Monday Night Ratings War, the nWo, company defections, briefly covers the fall of WCW, hits on the sex scandals, the steroid trials, several failure's of McMahon's like the WBF and XFL, and the deaths of stars like Owen Hart and Brian Pillman along with the after effects.
This is a great book for the hardcore fans, a good book for the part-time fans, and even an interesting text for the non-fan. Non-fans will continue to judge the wrestling industry poorly after reading this book but it is informative and may change some views that see wrestling as a circus of the ridiculous. The book loses a star in ratings because there are a number of historical inaccuracies in it which the devoted fan will easily find.
Vince Mc Mahon is God.......2005-11-12
This book learned me a lot of things about the wrestling business,as ruthless and even meaner than any other kind of business. Now mister McMahon rules supreme over the world he created. The wrestling world! He doing so by fighting nose to nose against billionaire Ted's WCW and their seemingly endless cash ressource. Being the underdog in the Monday Night War didn't prevent mister McMahon to buy at low price the folding WCW a couple of years later. And now, just to seal his aura of domination. Former nemesis Eric Bishoff and Paul Heyman are on the payroll of WWE.
It's amazing to see how much Genius Ambition Dedication mister McMahon was and still is. This book relates the story of success of a small regional promoter who build an Empire by himself. This book illustrates the way he goes to the top; which mean as he once said, becoming a billionaire in order to beat down a billionaire. He also said on a Raw segments that an individual need three qualities to succeed in business: killer instinct, mind manipulation, and marketing savvy. Three categories in which he excels as demonstrated in this book.
Mister McMahon monopolized this business by being a ruthless and merciless predator by purchasing others territories' headliners. Later, WCW tried to serves McMahon a taste of his own medecine. But their lack of creativity and direction was their downfall. All the money in the world couldn't challenge mister McMahon astuteness in the long run.
A plus for every aficianados like me who always want to know more about the backstabbing business of professional wrestling.
Long life WWE and thank you mister McMahon for the entertainment!
Average customer rating:
- Typical Chomsky.
- the truth doesnt hurt, it kills
- Thomas Jefferson's fears realized...
- Good Illustration of a Famous Guy's Perspectives
- Informative
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Secrets, Lies, and Democracy (Real Story Series)
Noam Chomsky , and
David Barsamian
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ASIN: 1878825046 |
Book Description
These interviews, conducted in 1993 and 1994, touch on a range of domestic and international topics from corporate welfare and free trade to gun control and religious fundamentalism
Customer Reviews:
Typical Chomsky........2006-06-06
Typical Chomsky; too general and vague to be thought provoking. His usual template, elite vs. populace, is applied to everything. There is no frame of reference nor explaining the dynamics of the situation. His references are nill. If people want to educate themselves on a particular topic, read material that is complete and indepth.
the truth doesnt hurt, it kills.......2006-05-03
he never fails to amaze me. chomskey is the middle-man between near-unobtainable knowledge and the interested public. Anyone who wants to really know the truth and not just a bunch of impartial, unjustified and most often distorted lies, pick up a chomskey book and read.
Thomas Jefferson's fears realized..........2004-09-28
This is an interesting pamphlet of interviews by David Barsamian with Noam Chomsky, which covers a wide collection of topics from defective democracy, health care, religious fundamentalism, the CIA and the media.
The central thrust of these interviews focuses on the corporatization of our democratic system. In one interview, Chomsky cites Thomas Jefferson's warning or fear, made at the end of his life, stating, that, the elites, aristocrats, "fear and distrust of the people, and wish to draw all powers from them into the hands of the higher classes." Democrats on the other hand, "identify with the people, have confidence in them, cherish and consider them as the most honest and safe, although not the most wise, depository of the public interest." What Jefferson was saying is that the people should have the reigns of power; we should be in control, and not the centralized, powerful elites. Jefferson's greatest fear was the "banking institutions and monied incorporations" (big business) and if they were allowed to influence politics, they would eventually run the entire show, benefiting the few at the exclusion of the majority. It is here, throughout this text, that Chomsky offers several examples how corporate America and big business internationally, influence our democratic system where, economically the "little guy' suffers while big business gets bigger as our basic wages plummet. In other terms, the rich get richer, the gap between rich and poor widens and only the few benefit.
One has only to look at the statistical indicators of countries around the world, comparing rich and poor sovereign states to see that nothing is changing for the better in developing countries but steadily getting worse, while the small percentage of rich countries, ironically exploiting these poorer countries, are improving their wealth. The gap is widening, particularly over the past thirty years, doubling the wealth in the top twenty percent, while the low twenty percent has become much poorer. These statistics speak for themselves, and there are reasons for this dramatic shift in wealth.
Politicians' incestuous connection to the corporate sector is well documented. Tax breaks for the rich, while the man or woman on basic wages supporting a family can pay, in some cases, more tax than a CEO. Our politicians for the obvious reasons protect the corporate sector: campaign contributions, personal investment, etc. Jefferson's fear and warning in the early 19th century against banking institutions and monied corporations involvement in politics has been realized.
Chomsky, in most cases, backs his arguments with statistical data and historical documentation that can be researched and checked by any interested individual. His words are never rhetorical, ad hominem arguments or self-righteous condemnations to push a personal agenda. He speaks about fact, revealing injustice and at times crimes against the common citizen that should not be ignored. This little book is a good starting point for further research into economic and international affairs.
Good Illustration of a Famous Guy's Perspectives.......2002-11-24
I disagree with Chomsky on many fronts to the point of irritation, finding that his research appears to consist primarily of what he reads (e.g., without talking to people more in the know), his opinions are slanted towards the most negative/conspiracy theory perspective (e.g., his interpretation on p. 56 that Clinton's encouragement of people to go to church is "...straightforward. If people devote themselves to activities that are out of the public arena, then we folks in power will be able to run things the way we want"), and he generally complains without recognizing the full picture (for instance, his prediction on p. 20 that Alabama's offering tax breaks to Daimler Benz would have negative consequences for most of its citizens, despite more recent aftermath reports that Alabama significantly benefitted) or offering a better alternative. But this book is a good readable summary of some of his views, and he does have a few good points (such as, how people are distracted from participating in democracy--though Chomsky misses the extent to which less intellectual people are not interested in participating--and the extent to which people need to organize to get political power (though the list of organizations at the conclusion of the book is wide-ranging, and emphasis is placed upon the groups' stated missions without recognition of their tactics, some of which are highly questionable).
Informative.......2001-04-23
This book gives a LOT of information at a very understandable writing level. A lot is talked about the US's involvement with other nations and, how it also helped the nazi's and other things like that. It's very interesting. Somethings were talked about more than others though, and not completely explained, but for the most part, it's pretty well explained.
Book Description
The Real Story Series is based on a simple idea--political books don't have to be boring. Short, well-written and to the point, Real Story books are meant to be read.
In these fact-filled, illusion-shattering masterpieces, the man the "New York Times" called "arguably the most important intellectual alive," explains why "what the public wants is called 'politically unrealistic.' Translated into English, that means power and privilege are opposed to it."
Normally somewhat difficult to read, Chomsky is at his most accessible in his speeches and interviews, and that's what these books are compiled from. Here are some examples of what he has to tell you:
In 1970, about 90% of international capital was used for trade and long-term investment-more or less productive things--and 10% reserved for speculation. By 1990, those figures were reversed.
Haiti, a starving island, is exporting food to the U.S.--about 35 times as much under Clinton as under Bush.
The gap between how much income is held by the richest and poorest 20? has increased dramatically over the past 30 years--about double for rich vs. poor countries and far more for rich vs. poor people.
Customer Reviews:
Towards greater inequalities.......2007-04-15
This trilogy gives a fair view of N. Chomsky's clinical vision on the US and the world.
He rightly sees the US as a business-run society, where the political parties reflect the interests of big corporations. The main aim of those corporations is higher market share and profits, not job creation or a better life for workers. An important factor in business profitability is the Pentagon and its military budget.
The powerful, the owners of those corporations, don't want to be subjected to democracy. They want an obedient, passive population of consumers and political spectators. This policy is successfully implemented through control of the media (`the general population doesn't know what's happening, and it doesn't know that it doesn't know').
The aim of US foreign policy was not to impose a democracy or respect for human rights or to increase living standards (a cardinal factor for the control of demographic tendencies). On the contrary, the US consistently opposed democracy if the results couldn't be controlled. Through covert (intelligence agencies) or military intervention the US (tried to) crush independent and popular forces that might bring about meaningful democracy (for those in power, `a virus' that would infect other countries and regions). Chomsky mentions interventions in Laos, Vietnam, Indonesia, the Philippines, Colombia, the Dominican Republic, Guatemala, Chili, Panama, Grenada, El Salvador, Nicaragua, Iraq, Iran, Yugoslavia, Greece and Italy.
In the US and worldwide, he sees considerable increases in inequality. In the US, real wages are declining since the 1960s and working conditions are worsening.
However, this book contains also some inaccuracies. N. Chomsky underestimated the democratic importance of internet and also its business impact (skilled information workers don't have to emigrate). He thought that biotechnology and genetic engineering would become the major investment focuses of the future, not military expenditures (today 50 % of the total US budget).
His analysis of the oil price hike in the 1970s is not correct (see W. Engdahl) and the main aim of speculative capital is quick gains (results are published every three months).
It is evident that in three small books one cannot fully evaluate international institutions or dismember philosophical problems. For criticism of GATT, IMF and World Bank I recommend the books of J. Stiglitz, and for a study of human nature and the roots of racism the works of R. Dawkins.
Ultimately, what can ordinary people do in order to influence the political process: first of all, vote (elections matter), also demonstrate (cause of the end of the Vietnam War) and divulge your opinion.
These books are written by a superbly free mind. We need Chomsky's voice. Highly recommended.
Thoughtful short work.......2002-07-30
more of a compendium of short interviews than indepth analysis but once again provides some thought provoking ideas for anyone interested in the world around them and if your're not, WHY NOT?
short interesting books on foreign policy and trade.......2002-06-09
The chomsky trilogy consists or three books from chomsky. They cover issues that really brought out by the media. They focus on U.S. foreign policy that many people may not be aware of it like nicauraga and hati. He deals with how coporations and strong anti-communist feeling influenced the policy. In addition, the books cover trade agreements like NAFTA and GATT and how they are influenced by corporations and turning parts of the industrialized world into the third world.
Some Good Points.......2002-04-24
In Chomsky's democracy, there is no passive citizens. Everyone will have to think and participate. And if you think about the some of the statements in this book, you begin to wonder. It's a good start when you embark on seriously reflecting on the nature of the world around us.
On the other hand, the reader whould do well to, as the first exercise, think about some of the things said in the book. For example, on p.99, it was mentioned by on of the questioners that "The United Sates, with 5% of the world's population, consumes 40% of the world's resources...." At the same time, on p.38, the author laments that "Real wages has been declining since the 1960's" in talking about the Third-Worldization of America. Does anyone not suspect that if Americans are any richer than they are now, they would not consume merely 40%, but maybe 50%, 60% or more, of the world's resources? Is it not implicit in the author's lament his horror at the thought of living a style not on the same level as the United States, when in fact, these other countries are living a more ecological balanced life? Yes, counter the defenders, but, it's possible for us to make more money and consume less. Really? What is the motivation to make money but to consume. And is it feasible at all that economic growth, the only source of wage growth, can be achieved without using up some resources of the world? A society where there is no farmer, no hunter but everyone is a lecturer, who does not pollute air, does not cut down trees, does not kill animals for food, does not exist.
In "Media Control", the same author talked about "manufacturing consent" and having "to turn to the technique of propaganda" by the government, as early as the Creel Commission to Americans to go in to World War I. In another breath, he writes in p.36 of this book, "the media contribute to the sense that the government is the enemy and they suppress the sources of real power in the society, which lie in the totalitarian institutions - the corporations, now international in scale - that control the economy and much of our social life." How is that possible? Did the Big Brother slip somewhere for the "controlled" media to attack it's own master?
Nevertheless, Chomsky is right to think that there is "a lot of power behind" the theory put forth by Thomas Ferguson, who believes that "the state is controlled by coalitions of investors who join together around some common interests." So, he is against Big Business. But, somewhat he is not against Big Government, for he thinks it's OK that the health care be in the hand of the government, for example.
He is only against the government when it comes to foreign policies. And here he is at his most consistent, as he describes one event after another, from the softball plants in Haiti, to Nicaragua, German POW's, Chile and Russia.
THE US POLICY OF AGGRESSION UNCOVERED!.......2002-01-20
In the past, the US was loved and respected in the world for symbolysing freedom, democracy and justice and for its educational humanitarian missions in many countries.
Regretfully, since WW2 it is increasingly identified with a foreign policy of domination, military aggresion, and glaringly immoral/unfair double standards particularly in the Middle East where its direct or indirect(through Israel) victims have been the Palestinian, Lebanese and Iraqi people.
Average customer rating:
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Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces
Walter Benz
Manufacturer: Birkhäuser Basel
ProductGroup: Book
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ASIN: 3764373717 |
Book Description
This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts.
Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.
Book Description
Which Everyday Idols Are Holding You Captive?
FOOD. BUSYNESS. IMAGE. POSSESSIONS. ACHIEVEMENT. APPROVAL. CONTROL. PERFECTIONISM. ATTENTION. HAPPINESS. BEING RIGHT. "PERFECT" RELATIONSHIPS. INDEPENDENCE. REVENGE. SELF-PITY. LOVE. SELF-RIGHTEOUSNESS.
Like most women, you probably have a life filled with modern-day "idols" that attempt to steal your attention and affection from God. Innocent-seeming idols like chocolate, thighs of iron, and a home that rivals Martha Stewart's. Things you turn to first, before turning to God, when you long for comfort, affirmation, self-worth, or love.
You know that God is the answer to all your needs. But then you have a fight with your husband, and that cheesecake in the fridge starts calling your name. You stay home from a women's retreat because your wardrobe is (literally) from the last century. You desperately wish that your house or hair or kids were as nice as your friend's (or anybody else's).
Customer Reviews:
Most helpful, honest book I've read in a long time.......2004-07-07
This book was great! It was honest, pointed and exactly what I needed to hear! I read it last year, and was so excited i wrote to the author, Nancy Kennedy. (I've NEVER written to an author or anything before!) She wrote back to me! How exciting to a 26 year old new SAHM with cabin fever! : ) I've used her note as a bookmark since I received it. I'm on my 4th read thru; sometimes I just skip to the chapter I need to read at that time. If you are thinking of reading this book- do it!
Funny, scriptural, and SO meaningful.......2003-07-26
Nancy Kennedy teaches with simple stories that have BIG meanings. (Hmmm...reminds me of another teacher...) I was attracted by the humor of this book and was held by its truth--which is repeatedly confirmed in the many, many scriptural references. I'm sharing this book (and her others) with my friends who are enjoying Mrs. Kennedy's writing as much as I do.
Sorry I bought this book.......2001-09-08
What a cute title! What a terrible book. I couldn't finish it, I felt embarrassed for Nancy Kennedy. She seems like a very nice person but holy cow! What a warped place this would be if all women believed as she does. God bless her!
Average customer rating:
- An excellent introduction to the topic of real simple Lie algebras
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Lectures on Real Semisimple Lie Algebras and Their Representations (ESI Lectures in Mathematics & Physics)
Arkady L. Onishchik
Manufacturer: Amer Mathematical Society
ProductGroup: Book
Binding: Paperback
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ASIN: 3037190027 |
Book Description
In 1914, E. Cartan posed the problem of finding all irreducible real linear Lie algebras. Iwahori gave an updated exposition of Cartan's work in 1959. This theory reduces the classification of irreducible real representations of a real Lie algebra to a description of the so-called self-conjugate irreducible complex representations of this algebra and to the calculation of an invariant of such a representation (with values $+1$ or $-1$) which is called the index. Moreover, these two problems were reduced to the case when the Lie algebra is simple and the highest weight of its irreducible complex representation is fundamental. A complete case-by-case classification for all simple real Lie algebras was given in the tables of Tits (1967). But actually a general solution of these problems is contained in a paper of Karpelevich (1955) that was written in Russian and not widely known.
The book begins with a simplified (and somewhat extended and corrected) exposition of the main results of Karpelevich's paper and relates them to the theory of Cartan-Iwahori. It concludes with some tables, where an involution of the Dynkin diagram that allows for finding self-conjugate representations is described and explicit formulas for the index are given. In a short addendum, written by J. V. Silhan, this involution is interpreted in terms of the Satake diagram.
The book is aimed at students in Lie groups, Lie algebras and their representations, as well as researchers in any field where these theories are used. Readers should know the classical theory of complex semisimple Lie algebras and their finite dimensional representation; the main facts are presented without proofs in Section 1. In the remaining sections the exposition is made with detailed proofs, including the correspondence between real forms and involutive automorphisms, the Cartan decompositions and the conjugacy of maximal compact subgroups of the automorphism group.
Published by the European Mathematical Society and distributed within the Americas by the American Mathematical Society.
Customer Reviews:
An excellent introduction to the topic of real simple Lie algebras.......2006-04-23
The main purpose of these notes is to give a self-contained and complete exposition of the representation theory of real semisimple Lie algebras. Although various texts on the topic exist, the originality of this small book is the elegance in the exposition and the presentation of some important facts that are absent in other treatises or only enumerated without further comment. Written by a prestigious expert in Lie theory, the text only demands a standard knowledge in the theory of complex Lie algebras and groups, and constitutes therefore an excellent text as a complement to an advanced course on the classification of complex semisimple Lie algebras and their representation theory.
The problem of classifying real simple and semisimple Lie algebras and their representations arises from the geometry of homogeneous spaces, and the first results in this direction were developed by E. Cartan himself in 1914. Using the more standardized algebraic theory and the work of Weyl, the study of real simple Lie algebras and groups was later expanded by various authors in order to develop a self-contained theory in analogy to the complex case. This work accomplishes this objective perfectly, and also pays homage to the important work of the late Fridrikh Izrailevich Karpelevich , who already solved many problems in the representation theory of real simple Lie algebras. However, these papers are unfortunately not widely known in the literature, and various of his results were later rediscovered by other authors.
The text is divided into nine sections, which present the main results with detailed proofs and illustrated with examples using the special simple algebra sl(n,C). The choice of this algebra is justified by the role it plays in the characterization of self-dual complex irreducible representations of real forms. For the remaining algebras the reader is led to the references.
The first section reviews the classical theory of semisimple complex Lie algebras, and fixes the notation that will be used in later chapters. The main material on compact groups that will be applied in the obtainment of real forms is also briefly presented, such as the theorem of Weyl. As recopilatory chapter, no proofs are given at this stage.
The second section deals with the complexification and realification of real and complex Lie algebras, respectively. Two important examples of real forms of complex semisimple Lie algebras are introduced: the real normal form, which can intuitively be interpreted as the algebra obtained by restriction of scalars and the compact form, which will be central for the construction of the remaining non-compact real forms. The first structural results concerning real forms are presented, namely, that real forms of simple complex algebras are simple, while complexification of real simple algebras are either simple or semisimple complex algebras [the insertion of the classical Lorentz algebra would have been welcomed after example 4]. The third section introduces the main tool used in the classification of real forms, the involutive automorphisms of a complex semisimple algebra and its correspondence with the real forms. It follows in particular that the compact form is unique. In order to describe this correspondence, the next section is devoted to various technical results concerning the automorphisms of complex semisimple algebras. Endowed with this machinery, the Cartan decomposition is discussed in detail. The conjugacy theorem of maximal compact subgroups of the adjoint linear group Int(g) is proved. Section 6 is devoted to an important problem which often appears in representation theory: given a homomorphism of complex semisimple Lie algebras f: ĝ →ĥ, which real forms of ĥ contain the image by f of some real form of ĝ? A satisfactory answer to this problem is given by means of the involutive automorphisms corresponding to the real forms. The material of this section follows the original work of F. I. Karpelevich in the beginning fifties . The material previously developed in chapter 3 concerning hermitean vector spaces is applied. Introducing a special class of morphisms, denoted S-homomorphisms , the result is sharpened. The seventh section devotes to the extension problem for irreducible representations for the case of the special linear Lie algebra sl(n,R). Special attention is devoted to the Karpelevich index, and the original formulae for computing this invariant are generalized to arbitrary involutive automorphisms. These results are applied in section 8 to classify explicitly the irreducible real representations in terms of highest weights, following the outline used by Iwahori in 1959. More precisely, real representations divide into two classes depending on the existence or not of an invariant complex structure. The last section, written by J. ?ilhan, presents an alternative classification by means of Satake diagrams, i.e., a generalization of the classical Dynkin diagram based on the introduction of two colors and arrows relating vertices of one color. It is described how to read off the involutions using these diagrams, and a characterization of self-dual complex irreducible representations is obtained. Additional material is presented in tabulated form at the end of this section.
Resuming, this book is very welcome reference on real simple Lie algebras, and has the innovation of presenting material that is distributed in many technical papers in a compact and effective way. It should be expected that this work will become a classic on the topic among the specialists in Lie algebras.
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Dam Lies and Other Statistics: Taking the Measure of Irrigation in China, 1931-91 (East-West Center Occasional Papers. Environment Series, No 18)
James E. Nickum
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The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation (Progress in Mathematics)
Andre Unterberger
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Book Description
The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers. Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, in harmonic analysis, or in mathematical physics.
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Hardy Spaces on Homogeneous Groups. (MN-28) (Mathematical Notes)
Gerald B. Folland , and
Elias M. Stein
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The Real Rules: Sex, Lies, God, Marriage, Polygamy, Adultery, Virgin Girls, Real Men, Homosexuals, Lesbians, Feminists, AIDS-Racism, Marijuana & Other Green vegetatio
Jimmy Ricard
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