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Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groups


Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groups Cover

ISBN13: 9780199202515
ISBN10: 0199202516
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Synopses & Reviews

Publisher Comments:

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.

Table of Contents

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



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cgeorgak, December 9, 2007 (view all comments by cgeorgak)
The best among all books on Lie Groups that provides an an effective and concrete introduction to Lie Groups. Rossman starts almost from scratch and gets to the heart of the subject while building the essential tools required along the way and following an original approach invented by the author. Anyone who takes the time to learn Lie Groups from this text will find himself amply rewarded.
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Product Details

Rossmann, Wulf
Oxford University Press, USA
Rossman, Wulf
null, Wulf
Algebra - Linear
Mathematics | Pure Mathematics
Mathematics-Linear Algebra
Edition Description:
bonded leather black indexed 6261RRL
Oxford Graduate Texts in Mathematics
Series Volume:
Publication Date:
Grade Level:
Professional and scholarly
9 pt. type
9.24x6.04x.58 in. .94 lbs.

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Linear Algebra

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