ENGLISH

Lie groups and Lie algebras.Chapters 7-9

By Nicolas Bourbaki

Book information

Publisher
Springer
Year
2004
ISBN
9783540434054, 3540434054
LCC
QA387 .B65213 2004
Open Library ID
OL22625848M
Language
english
Format
PDF
Filesize
3 MB (2751452 bytes)
Series
Elements of mathematics
Edition
1
Pages
439\439
Topic
Mathematics Algebra
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

This is the English translation of Bourbaki's text Groupes et Algebres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-50218-1) and 4 to 6 (3-540-42650-7) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

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