Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)
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Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)
Book Details
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Publisher: Springer
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Author: N. Bourbaki
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Language: English
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Edition: First Edition
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ISBN: 9783540688518
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Pages: 445
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Cover: Paperback
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Dimensions: 9.2 x 6.1 x 1.0 inches
About The Book
Lie Groups and Lie Algebras: Chapters 7–9 by N. Bourbaki is the final volume in the legendary mathematical series covering the theory of Lie groups and Lie algebras. This softcover reprint in English provides a rigorous and detailed exposition of advanced topics including the structure and representation theory of semi-simple Lie algebras and compact Lie groups, completing the material introduced in Chapters 1 to 6.
Chapter 7 explores Cartan subalgebras, regular elements, and conjugacy theorems, forming the backbone of the structure theory of Lie algebras. Chapter 8 shifts focus to split semi-simple Lie algebras, detailing their root systems, and develops a comprehensive treatment of finite-dimensional modules, culminating in Weyl's character formula and the theory of Chevalley orders.
Chapter 9 is a masterful treatment of compact Lie groups, beginning with maximal tori, Weyl groups, and their root systems, and progressing to an in-depth study of representation theory. It skillfully integrates harmonic analysis through applications of integration, establishing Weyl’s formula in the context of compact groups. The chapter concludes with a study of group actions on manifolds, extending the utility of Lie theory into geometric and topological realms.
Renowned for its mathematical precision and depth, this volume is an indispensable reference for researchers, graduate students, and professionals in pure mathematics, theoretical physics, and differential geometry, and serves as the most comprehensive and authoritative source on the subject of Lie groups and algebras.
