Lie Groups Beyond an Introduction

ISBN-10: 0817642595

ISBN-13: 9780817642594

Edition: 2nd 2002 (Revised)

Authors: Anthony W. Knapp

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From reviews of the first edition:"The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS"This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." -- Mathematica"Each chapter begins with an excellent summary of the content and ends with an exercise section... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." -- Publicationes MathematicaeLie 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.
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Book details

Edition: 2nd
Copyright year: 2002
Publisher: Birkhauser Boston
Publication date: 8/21/2002
Binding: Hardcover
Pages: 812
Size: 6.50" wide x 9.50" long x 1.75" tall
Weight: 3.234
Language: English

Preface to the Second Edition
Preface to the First Edition
List of Figures
Prerequisites by Chapter
Standard Notation
Introduction: Closed Linear Groups
Lie Algebras and Lie Groups
Complex Semisimple Lie Algebras
Universal Enveloping Algebra
Compact Lie Groups
Finite-Dimensional Representations
Structure Theory of Semisimple Groups
Advanced Structure Theory
Integration
Induced Representations and Branching Theorems
Prehomogeneous Vector Spaces
Tensors, Filtrations, and Gradings
Lie's Third Theorem
Data for Simple Lie Algebras
Hints for Solutions of Problems
Historical Notes
References
Index of Notation
Index
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