Lie algebras and Lie groups : 1964 lectures given at Harvard University
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Bibliographic Information
Lie algebras and Lie groups : 1964 lectures given at Harvard University
(Lecture notes in mathematics, 1500)
Springer-Verlag, c1992
2nd ed
- : gw
- : us
Available at / 115 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||150078894612
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: gw10092700308,10092700753,
: Berlin410.8-L49-1500//411.68927003044 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: Berlindc20:512/se682070223306
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Note
Originally published: New York : W.A. Benjamin, 1965
Corr. 5th printing: 2006
Bibliography: p. [161]-162
Includes index
Description and Table of Contents
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 (R)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).
Table of Contents
Lie Algebras.- Lie Algebras: Definition and Examples.- Filtered Groups and Lie Algebras.- Universal Algebra of a Lie Algebra.- Free Lie Algebras.- Nilpotent and Solvable Lie Algebras.- Semisimple Lie Algebras.- Representations of .- Lie Groups.- Complete Fields.- Analytic Functions.- Analytic Manifolds.- Analytic Groups.- Lie Theory.
by "Nielsen BookData"