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Representations of Lie algebras : an introduction through gln Preview this item
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Representations of Lie algebras : an introduction through gln

Author: Anthony Henderson
Publisher: Cambridge : Cambridge University Press, 2012.
Series: Australian Mathematical Society lecture series, 22.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest  Read more...
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Details

Document Type: Book
All Authors / Contributors: Anthony Henderson
ISBN: 9781107653610 1107653614
OCLC Number: 785872028
Description: ix, 156 pages : illustrations ; 23 cm.
Contents: 1. Motivation: representations of Lie groups --
2. Definition of a Lie algebra --
3. Basic structure of a Lie algebra --
4. Modules over a Lie algebra --
5. The theory of sl₂-modules --
6. General theory of modules --
7. Integral gln̳-modules --
8. Guide to further reading --
Appendix: solutions to the exercises.
Series Title: Australian Mathematical Society lecture series, 22.
Responsibility: Anthony Henderson, School of Mathematics and Statistics, University of Sydney.

Abstract:

A fresh undergraduate-accessible approach to Lie algebras and their representations.  Read more...
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'This short book develops the standard tools (special bases, duality, tensor decompositions, Killing forms, Casimir operators ...) and aims for a single result: the classification of integral modules Read more...

 
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