Theory of Lie Groups (Dover Books on Mathematics) by Claude Chevalley (PDF)

Description

“Chevalley’s most important contribution to mathematics is certainly his work on group theory. . . . [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades.” — Bulletin of the American Mathematical Society Suitable for advanced undergraduate and graduate students of mathematics, this enduringly relevant text introduces the main basic principles that govern the theory of Lie groups. The treatment opens with an overview of the classical linear groups and of topological groups, focusing on the theory of covering spaces and groups, which is developed independently from the theory of paths. Succeeding chapters contain an examination of the theory of analytic manifolds as well as a combination of the notions of topological group and manifold that defines analytic and Lie groups. An exposition of the differential calculus of Cartan follows and concludes with an exploration of compact Lie groups and their representations.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Classic on Lie Theory every one who likes Lie theory should have a copy

⭐Claude Chevalley’s “Theory of Lie Groups” was published in 1946. It is the first formulation of the concept of Lie Groups. Although there are some spots where more recent texts on Lie groups are cleaner, there are many where the exposition still remains the standard. It was and remains a classic. The first two chapters alone are beautiful treatments of preliminary matters and are well worth the purchase price.Of course, this book doesn’t treat the major advances in Lie theory that occurred after its publication, but its publication, along with Chevalley’s further publications on Lie theory inspired a whole generation of mathematicians and physicists.If you are a physicist, there are expositions that may provide a simpler path to the applications of Lie theory to physics. Lie theory has always been a source of division between the way mathematicians understand the subject. But the best physicists have always tried to understand the mathematicians’ point of view and have been amply rewarded. The same can be said for mathematicians who have also been rewarded for understanding how physicists apprehend Lie theory.

⭐This book is very sexy. Even the name, Claude Chevalley, ooh la la. I can’t wait to be French someday and master the language so I can Chevalley my way into the math departments and **** some hot French girls with my mathematical prowess. I kid. But really. There are differential forms in this book, there’s everything you’re supposed to need. But it’s not pretty in the modern notation used today. It reads very old and antiquated, like they first invented Lie Groups and it’s like ok, no go, do something with them mathematicians and scientists. And do something they did! Out came the Standard Model, and Fibre Bundle Geometry! Ooh La La! But after all that, this book is very dated and you will want something more grounded to these very important applications of the theory, with particular attention to the representations of SU(n) and the Lorentz group.

⭐表紙も傷ひとつなく、中もとても綺麗な状態でした。やはり海外からの取り寄せということで、到着まで時間はかかりましたが、買ってよかったと思います。

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