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Lie groups

Autor: J J Duistermaat; Johan A C Kolk
Verlag: Berlin ; New York : Springer, ©2000.
Serien: Universitext.
Ausgabe/Medienart   Gedrucktes Buch : EnglischAlle Ausgaben und Medienarten anzeigen
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"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  Weiterlesen…
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Medienart: Internetquelle
Dokumenttyp Buch, Internet-Ressource
Alle Autoren: J J Duistermaat; Johan A C Kolk
ISBN: 3540152938 9783540152934
OCLC-Nummer: 42619683
Beschreibung: viii, 344 pages : illustrations ; 24 cm.
Inhalt: 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.
Serientitel: Universitext.
Verfasserangabe: Johannes J. Duistermaat, Johan A.C. Kolk.
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Abstract:

It 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 compact Lie groups and their  Weiterlesen…

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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 Weiterlesen…

 
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