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Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9
Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9
Date: 03 Feb 2007, 21:52
(Elements of Mathematics)
3540434054, Pages: 434

This is the English translation of Bourbaki's text Groupes et Algèbres de Lie, Chapters 7 to 9. It

completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) 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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