Lie groups an introduction through linear groups

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 develo...

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Tác giả chính: Rossmann, Wulf
Tác giả khác: Wulf Rossmann
Ngôn ngữ:Undetermined
English
Được phát hành: Oxford Oxford University Press 2002
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Thư viện lưu trữ: Trung tâm Học liệu Trường Đại học Trà Vinh
Miêu tả
Tóm tắt: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
Mô tả vật lý:265 p.
ill.
25 cm
số ISBN:0199202516
9780199202515