عنوان

Lie groups : an introduction through linear groups

4588

English

Rossmann, Wulf

8491-

Lie groups : an introduction through linear groups

Oxford

Oxford University Press

2002

x, 265 p.: ill. ; 25 cm

Oxford graduate texts in mathematics; 5

Includes bibliographical references )p. 258- 260( and index

Wulf Rossmann

Machine generated contents note: 1 The exponential map 1 -- 1.1 Vector fields and one-parameter groups of -- linear transformation 1 -- 1.2 Ad, ad, and dexp 21 -- 1.3 The Campbell-Baker-Hausdorff series 22 -- 2 Lie theory 03 -- 2.1 Linear groups: definitions and examples 03 -- 2.2 The Lie algebra of a linear group 44 -- 2.3 Coordinates on a linear group 35 -- 2.4 Connectedness 16 -- 2.5 The Lie correspondence 66 -- 2.6 Homomorphisms and coverings of linear groups 87 -- 2.7 Closed subgroups 78 -- 3 The classical groups 19 -- 3.1 The classical groups: definitions, connectedness 19 -- 3.2 Cartan subgroups 701 -- 3.3 Roots, weights, reflections 511 -- 3.4 Fundamental groups of the classical groups 121 -- 4 Manifolds, homogeneous spaces, Lie groups 231 -- 4.1 Manifolds 231 -- 4.2 Homogeneous spaces 341 -- 4.3 Lie groups 251 -- 5 Integration 561 -- 5.1 Integration on manifolds 561 -- 5.2 Integration on linear groups and -- their homogeneous spaces 171 -- 5.3 Weyl's integration formula for U)n( 971 -- 6 Representations 981 -- 6.1 Representations: definitions 981 -- 6.2 Schur's lemma, Peter-Weyl theorem 791 -- 6.3 Characters 502 -- 6.4 Weyl's character formula for U)n( 212 -- 6.5 Representations of Lie algebras 322 -- 6.6 The Borel-Weil theorem for GL)n, C( 232 -- 6.7 Representations of the classical groups 732 -- Appendix Analytic Functions and Inverse -- Function Theorem 052

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