Lie Groups Beyond an Introduction

by Anthony W. Knapp

"Lie Groups Beyond an Introduction" takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond. Progress in Mathematics, Volume 140

Genres: Mathematics, Algebra, Science

604 pages, Hardcover

First published January 1, 1996

Reviews

[Max]

The best book on the topic.

[Ryan]

Indispensable for anyone wishing to understand Lie Groups, algebras and root systems. I wish some examples were more developed and a bit more explicit at times, but Knapp comes with an excellent index and list of notation that makes navigation a breeze.