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Other titles in the Oxford Graduate Texts in Mathematics series:
Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groupsby Wulf Rossman
Synopses & Reviews
This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.
Book News Annotation:
An advanced undergraduate and beginning graduate textbook introducing the theory of Lie groups starting straight from calculus and linear algebra and picking up differential geometry, functional analysis, and general topology on the way.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
An introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. Covering the essentials of the subject, starting from basic undergraduate mathematics, it proceeds through the fundamentals of Lie theory up to topics in representation theory.
Includes bibliographical references (p. 258-260) and index.
Table of Contents
1. The Exponential Map
2. Lie Theory
3. The Classical Groups
4. Manifolds, Homogeneous Spaces, Lie Groups
Appendix: Analytic Functions and Inverse Function Theorem
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