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Lie groups

Author: J J Duistermaat; Johan A C Kolk
Publisher: Berlin ; New York : Springer, ©2000.
Series: Universitext.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This is a (post)graduate textbook an 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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J J Duistermaat; Johan A C Kolk
ISBN: 3540152938 9783540152934
OCLC Number: 42619683
Description: viii, 344 p. : ill. ; 24 cm.
Contents: 1. 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 --
2. 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 --
3. Compact Lie Groups. Centralizers. The Adjoint Action.
Series Title: Universitext.
Responsibility: Johannes J. Duistermaat, Johan A.C. Kolk.
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Abstract:

A (post) graduate text that analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of  Read more...

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From the reviews: "This one is worth to read and to keep on your shelf! It presents the theory of Lie groups not only in the usual way of Lie algebraic treatment, but also from the global point of Read more...

 
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