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Lie Groups : An Introduction Through Linear Groups - Wulf Rossmann

Lie Groups

An Introduction Through Linear Groups

Hardcover Published: 1st February 2002
ISBN: 9780198596837
Number Of Pages: 276

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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.

`Rossmann adopts a new approach and works with arbitrary sets of invertible matrices closed under inversion and multiplication but with absolutely no topological assumptions.' Bulletin of the American Mathematical Society

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

ISBN: 9780198596837
ISBN-10: 0198596839
Series: Oxford Graduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 276
Published: 1st February 2002
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.0 x 16.1  x 1.8
Weight (kg): 0.5

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