Lie groups beyond an introduction / Anthony W. Knapp.

Format:

Book

Author/Creator:

Knapp, Anthony W., author.

Contributor:

Rosengarten Family Fund.

Series:

Progress in mathematics (Boston, Mass.) ; v. 140.

Progress in mathematics ; v. 140

Language:

English

Subjects (All):

Lie groups.

Lie algebras.

Representations of Lie groups.

Representations of groups.

Physical Description:

xv, 604 pages : illustrations ; 24 cm.

Place of Publication:

Boston : Birkhäuser, [1996]

Summary:

"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 expert: 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." -- Book Jacket.

Contents:

I. Lie Algebras and Lie Groups

II. Complex Semisimple Lie Algebras

III. Universal Enveloping Algebra

IV. Compact Lie Groups

V. Finite-Dimensional Representations

VI. Structure Theory of Semisimple Groups

VII. Advanced Structure Theory

VIII. Integration

App. A. Tensors, Filtrations, and Gradings

App. B. Lie's Third Theorem

App. C. Data for Simple Lie Algebras.

Notes:

Includes bibliographical references (pages 585-594) and indexes.

Current copyright fee: GBP34.00 22\1.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

0817639268

9780817639266

3764339268

9783764339265

OCLC:

34546072