Lie Groups Beyond an Introduction
Edition: 2nd 2002 (Revised)
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Description: 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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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $89.99
Copyright year: 2002
Publisher: Birkhauser Boston
Publication date: 8/21/2002
Size: 6.10" wide x 9.25" long x 1.75" tall
|Preface to the Second Edition|
|Preface to the First Edition|
|List of Figures|
|Prerequisites by Chapter|
|Introduction: Closed Linear Groups|
|Lie Algebras and Lie Groups|
|Complex Semisimple Lie Algebras|
|Universal Enveloping Algebra|
|Compact Lie Groups|
|Structure Theory of Semisimple Groups|
|Advanced Structure Theory|
|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|
|Index of Notation|