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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics) - Hardcover
Synopsis
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.
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About the Author
Wulf Rossmann is at University of Ottawa, Department of Mathematics and Statistics.
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Lie Groups: An Introduction Through Linear Groups Oxford Graduate Texts in Mathematics, Number 5.
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Oxford University Press, 2002
ISBN 10: 0198596839
ISBN 13: 9780198596837
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Lie Groups: An Introduction Through Linear Groups (Oxford Graduate Texts in Mathematics, 5)
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ISBN 10: 0198596839
ISBN 13: 9780198596837
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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics)
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ISBN 10: 0198596839
ISBN 13: 9780198596837
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Lie Groups : An Introduction Through Linear Groups
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Lie Groups : An Introduction Through Linear Groups
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Lie Groups (Hardcover)
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ISBN 10: 0198596839
ISBN 13: 9780198596837
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Hardcover. Condition: new. Hardcover. 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 thestructural 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 thesemethods. 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. An introduction the theory of Lie groups and their representations. It covers the essentials of the subject: it proceeds through the fundamentals of Lie theory up to topics in representation theory, such as the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780198596837
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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics, 5)
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Lie Groups : An Introduction Through Linear Groups
Published by
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ISBN 10: 0198596839
ISBN 13: 9780198596837
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