Lie Groups
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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.
- 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
- Appendices
- Hints for Solutions of Problems
- Historical Notes
- References
- Index of Notation
- Index.
- Autor: Anthony W. Knapp
- 2002, 2nd ed., 812 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817642595
- ISBN-13: 9780817642594
- Erscheinungsdatum: 21.08.2002
"Anthony Knapp's Lie Groups Beyond an Introduction, 2nd edition, is a beautiful introduction to this area of mathematics, appropriate for a variety different audiences.... The book is well-organized with concise, focused introductions to each chapter, a very thorough index of notation, and appendices.... In addition, there are hints to the hundreds of exercises, and a section on historical notes.... Knapp's writing is clear, and he avoids excessive notation. The first few chapters comprise a standard introductory course in Lie theory, while numerous second courses could be taught out of the later chapters. Its breadth of coverage and extensive tables also make the book a valuable reference for researchers in representation theory." -MAA Reviews (review of the second edition)
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