Lie Groups and Lie Algebras

Chapters 7-9
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ISBN-13:
9783540688518
Einband:
Paperback
Erscheinungsdatum:
30.09.2008
Seiten:
448
Autor:
N. Bourbaki
Gewicht:
674 g
Format:
235x155x24 mm
Sprache:
Englisch
Beschreibung:

This is the softcover reprint of 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 (978-3-540-69171-6) 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.
Cartan Subalgebras and Regular Elements.- Split Semi-simple Lie Algebras.- Compact Real Lie Groups.

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