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Lie algebras and Lie groups: 1964 lectures given at Harvard University (Mathematics lecture note series ; 2)

Jean Pierre Serre

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ISBN 10: 080538703X / ISBN 13: 9780805387032
Published by W. A. Benjamin, 1965
Used Condition: Good Hardcover
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First Edition. Rubbing to edges of soft cover book. Inked ownership Harry L. Morrison (1932-2002) late Prof. Physics, University of California, Berkeley, half-title page. No other markings in book. From the Introduction: 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 of Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-p-groups, etc. Bookseller Inventory # 3003852

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Bibliographic Details

Title: Lie algebras and Lie groups: 1964 lectures ...

Publisher: W. A. Benjamin

Publication Date: 1965

Binding: Hardcover

Book Condition:Good

About this title

Synopsis:

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).

Product Description:

This book reproduces J-P. Serre's 1964 Harvard lectures (formerly LNM 1500). The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.

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