Lie groups : an introduction through linear groups
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Bibliographic Information
Lie groups : an introduction through linear groups
（Oxford graduate texts in mathematics, 5）
Oxford University Press, 2002
Available at / 34 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:512.55/R7372080022042
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Note
Bibliography: p. 258-260
Includes index
Description and Table of Contents
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.
Table of Contents
- Preface
- 1. The exponential map
- 2. Lie theory
- 3. The classical groups
- 4. Manifolds, homogeneous spaces, Lie groups
- 5. Integration
- 6. Representations
- Appendix: Analytic Functions and Inverse Function Theorem
- References
- Index
by "Nielsen BookData"
