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

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

ISBN13: 9780199202515
ISBN10: 0199202516
Condition:
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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

References

Index

What Our Readers Are Saying

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Average customer rating based on 1 comment:

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

ISBN:
9780199202515
Author:
Rossmann, Wulf
Publisher:
Oxford University Press, USA
Author:
Rossman, Wulf
Author:
null, Wulf
Subject:
Algebra - Linear
Subject:
Mathematics | Pure Mathematics
Subject:
Mathematics-Linear Algebra
Edition Description:
bonded leather black indexed 6261RRL
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
5
Publication Date:
20060731
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
9 pt. type
Pages:
280
Dimensions:
9.24x6.04x.58 in. .94 lbs.

Related Subjects


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

Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groups New Trade Paper
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Product details 280 pages Oxford University Press, USA - English 9780199202515 Reviews:
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