9783540550082-3540550089-Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics (1500))

Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics (1500))

ISBN-13: 9783540550082
ISBN-10: 3540550089
Edition: 2nd
Author: Serre, Jean-Pierre
Publication date: 1992
Publisher: Springer
Format: Paperback 180 pages
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Book details

ISBN-13: 9783540550082
ISBN-10: 3540550089
Edition: 2nd
Author: Serre, Jean-Pierre
Publication date: 1992
Publisher: Springer
Format: Paperback 180 pages

Summary

Acknowledged authors Serre, Jean-Pierre wrote Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics (1500)) comprising 180 pages back in 1992. Textbook and eTextbook are published under ISBN 3540550089 and 9783540550082. Since then Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics (1500)) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal,.. This part has been written with the help of F.Raggi and J.Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x,y) under this map by [x,y) then the condition becomes for all x e k. [x,x)=0 2). (lx,II], z]+ny, z), x) + ([z,xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/,x).

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