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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics) - Softcover
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 in the Department of Mathematics and Statistics, University of Ottawa.
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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics)
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Lie Groups : An Introduction Through Linear Groups
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Lie Groups: An Introduction Through Linear Groups (eng)
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Lie Groups (Paperback)
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ISBN 13: 9780199202515
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Paperback. Condition: new. Paperback. 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 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. This new in paperback edition provides a clear introduction to the theory of Lie groups and their representations for advanced undergraduates and graduate students in mathematics. Starting from basic undergraduate level mathematics, the text proceeds through the fundamentals of Lie theory up to topics in representation theory. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780199202515
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