Item description for Lie Groups (Universitext) by J. J. Duistermaat & Johan A. C. Kolk...
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. The relations with algebraic and analytic models are also discussed. A review of the required background material is provided in appendices.
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Est. Packaging Dimensions: Length: 0.75" Width: 6.25" Height: 9.5" Weight: 1 lbs.
Release Date Mar 22, 2004
ISBN 3540152938 ISBN13 9783540152934
Availability 0 units.
More About J. J. Duistermaat & Johan A. C. Kolk
J. J. Duistermaat was born in 1942 and has an academic affiliation as follows - Universiteit Utrecht, The Netherlands.
Reviews - What do customers think about Lie Groups (Universitext)?
A Brilliant Book on Lie Groups Sep 17, 2000
I have read this book with great interest. It deals with the theory of Lie groups from the global point of view, not only the usual Lie algebraic treatment. Of particular originality is the theory of orbits for compact groups, an issue with many applications such as the patterns of symmetry breaking in elementary particle physics. I also particularly appreciated the chapter about the Borel-Weil theory of representations which does not seem to be available in textbooks. The style and breadth of the exposition will certainly make it an instant classic, a perfect complement to the Lie algebra texts by Humphreys or Jacobson. I also appreciated the emphasis on the differential geometric aspects of the subject. One regret is that the authors did not delve into the orbit theory of complex Lie groups and the link with geometric invariant theory.