Lie Groups: An Introduction Through Linear Groups

Paperback | June 29, 2006

byWulf Rossmann

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Lie Groups 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 andLie 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. Thefundamental 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 ongroups 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.

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From the Publisher

Lie Groups 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 andLie algebras is developed in its local and gl...

Wulf Rossmann is in the Department of Mathematics and Statistics, University of Ottawa.
Format:PaperbackDimensions:280 pages, 9.21 × 6.14 × 0.61 inPublished:June 29, 2006Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199202516

ISBN - 13:9780199202515

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Table of Contents

Preface1. The exponential map2. Lie theory3. The classical groups4. Manifolds, homogeneous spaces, Lie groups5. Integration6. RepresentationsAppendix: Analytic Functions and Inverse Function TheoremReferencesIndex

Editorial Reviews

`Rossmann's book is a gem ... His development has some elements that are new to me, and I regard those elements as a breakthrough in making elementary Lie theory more widely accessible.'A. W. Knapp, The American Mathematical Monthly