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Product details:
- Publisher OUP Oxford
- Date of Publication 10 January 2002
- ISBN 9780198596837
- Binding Hardback
- No. of pages276 pages
- Size 240x161x18 mm
- Weight 560 g
- Language English
- Illustrations numerous tables and figures 0
Categories
Short description:
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, such as the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.
MoreLong description:
This book is intended as 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 analysed 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, roots, 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.
The book benefits from a considerable number of exercises in each chapter. It is well worth considering as a course text.
Table of Contents:
Preface
The exponential map
Lie theory
The classical groups
Manifolds, homogeneous spaces, Lie groups
Integration
Representations
Appendix: Analytic Functions and Inverse Function Theorem
References
Index
