An Introduction to Lie Groups and Lie Algebras

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Cambridge University Press, Jul 31, 2008 - Mathematics - 222 pages
This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.
 

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Contents

2
5
Lie groups and Lie algebras
25
1
44
Representations of Lie groups and Lie algebras
52
Structure theory of Lie algebras
84
12
89
Complex semisimple Lie algebras
108
Root systems
132
Representations of semisimple Lie algebras
163
Overview of the literature
197
Appendix B Sample syllabus
210
Bibliography
216
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About the author (2008)

Alexander Kirillov, Jr, is an Associate Professor in the Mathematics Department, State University of New York, Stony Brook. His research interests are representation theory, Lie algebras, quantum groups, affine Lie algebras and conformal field theory.

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