Lie groups

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"This book is a (post)graduate textbook on Lie groups and Lie algebras. Its aim is to give a broad introduction to the field with an emphasis on using differential-geometrical methods, in the spirit of Lie himself. The structure of compact Lie groups is analyzed in terms of the action of the group on itself by conjugation. The book culminates in the classification of the representations of compact Lie groups and in their realization as sections of holomorphic line bundles over flag manifolds. T…

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Title Statements

Full title :Lie groups / J.J. Duistermaat, J.A.C. Kolk.

Summary

Edition Statements

Publication Date:2000

Publication Statements

Publisher(s):Springer
Place of Publication:Berlín
Language:eng
Publication Date:2000

The Physical Object

Description:VIII, 344 p. ; : 24 cm.

Edition Identifiers

ISBN:3540152938, 9783540152934
oclc:ocn639830761
LC Classification:QA387
Dewey Decimal:512.55

Preface -- Lie Groups and Lie Algebras: Lie Groups and their Lie Algebras; Examples; The Exponential Map; The Exponential Map for a Vector Space; The Tangent Map of Exp; The Product in Logarithmic Coordinates; Dynkin's Formula; Lie's Fundamental Theorems; The Component of the Identity; Lie Subgroups and Homomorphisms; Quotients; Connected Commutative Lie Groups; Simply Connected Lie Groups; Lie's Third Fundamental Theorem in Global Form; Exercises -- Proper Actions: Review; Bochner's Linearization Theorem; Slices; Associated Fiber Bundles; Smooth Functions on the Orbit Space; Orbit Types and Local Action Types; The Stratification by Orbit Types; Principal and Regular Orbits; Blowing Up -- Compact Lie Groups: Centralizers; The Adjoint Action; Connectedness of Centralizers; The Group of Rotations and its Covering Group; ... Representations of Compact Groups: ... Schur's Lemma; Averaging; The Peter-Weyl Theorem; ... Weight Exercises; The Borel-Weil Theorem ... -- Appendix.