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Media type:
Book
Title:
Lie groups
:
an introduction through linear groups
Contains:
Includes bibliographical references and index
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 12 -- 1.3 The Campbell-Baker-Hausdorff series 22 -- 2 Lie theory 30 -- 2.1 Linear groups: definitions and examples 30 -- 2.2 The Lie algebra of a linear group 44 -- 2.3 Coordinates on a linear group 53 -- 2.4 Connectedness 61 -- 2.5 The Lie correspondence 66 -- 2.6 Homomorphisms and coverings of linear groups 78 -- 2.7 Closed subgroups 87 -- 3 The classical groups 91 -- 3.1 The classical groups: definitions, connectedness 91 -- 3.2 Cartan subgroups 107 -- 3.3 Roots, weights, reflections 115 -- 3.4 Fundamental groups of the classical groups 121 -- 4 Manifolds, homogeneous spaces, Lie groups 132 -- 4.1 Manifolds 132 -- 4.2 Homogeneous spaces 143 -- 4.3 Lie groups 152 -- 5 Integration 165 -- 5.1 Integration on manifolds 165 -- 5.2 Integration on linear groups and -- their homogeneous spaces 171 -- 5.3 Weyl's integration formula for U(n) 179 -- 6 Representations 189 -- 6.1 Representations: definitions 189 -- 6.2 Schur's lemma, Peter-Weyl theorem 197 -- 6.3 Characters 205 -- 6.4 Weyl's character formula for U(n) 212 -- 6.5 Representations of Lie algebras 223 -- 6.6 The Borel-Weil theorem for GL(n, C) 232 -- 6.7 Representations of the classical groups 237 -- Appendix Analytic Functions and Inverse -- Function Theorem 250