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Lie algebras /
Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Chino |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1975]
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| Edición: | First edition]. |
| Colección: | International series of monographs in pure and applied mathematics ;
v. 104. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Lie Algebras; Copyright Page; Table of Contents; PREFACE; CHAPTER 1. BASIC CONCEPTS; 1.1. Lie algebras; 1.2. Subalgebras, ideals and quotient algebras; 1.3. Simple algebras; 1.4. Direct sum; 1.5. Derived series and descending central series; 1.6. Killing form; CHAPTER 2. NILPOTENT AND SOLVABLE LIE ALGEBRAS; 2.1. Preliminaries; 2.2. Engel's theorem; 2.3. Lie's theorem; 2.4. Nilpotent linear Lie algebras; CHAPTER 3. CARTAN SUBALGEBRAS; 3.1. Cartan subalgebras; 3.2. Existence of Cartan subalgebras; 3.3. Preliminaries; 3.4. Conjugacy of Cartan subalgebras.
- CHAPTER 4. CARTAN'S CRITERION4.1. Preliminaries; 4.2. Cartan's criterion for solvable Lie algebras; 4.3. Cartan's criterion for semisimple Lie algebras; CHAPTER 5. CARTAN DECOMPOSITIONS AND ROOT SYSTEMS OF SEMISIMPLE LIE ALGEBRAS; 5.1. Cartan decompositions of semisimple Lie algebras; 5.2. Root systems of semisimple Lie algebras; 5.3. Dependence of structure of semisimple Lie algebras on root systems; 5.4. Root systems of the classical Lie algebras; CHAPTER 6. FUNDAMENTAL SYSTEMS OF ROOTS OF SEMISIMPLE LIE ALGEBRAS AND WEYL GROUPS; 6.1. Fundamental systems of roots and prime roots.
- 9.3. Representations of the three-dimensional simple Lie algebraCHAPTER 10. REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS; 10.1. Irreducible representations of semisimple Lie algebras; 10.2. Theorem of complete reducibility; 10.3. Fundamental representations of semisimple Lie algebras; 10.4. Tensor representations; 10.5. Elementary representations of simple Lie algebras; CHAPTER 11. REPRESENTATIONS OF THE CLASSICAL LIE ALGEBRAS; 11.1. Representations of An; 11.2. Representations of Cn; 11.3. Representations of Bn; 11.4. Representations of Dn.
- CHAPTER 12. SPIN REPRESENTATIONS AND THE EXCEPTIONAL LIE ALGEBRAS12.1. Associative algebras; 12.2. Clifford algebra; 12.3. Spin representations; 12.4. The exceptional Lie algebras F4 and E6; CHAPTER 13. POINCAR�E-BIRKHOFF-WITT THEOREM AND ITS APPLICATIONS TO REPRESENTATION THEORY OF SEMISIMPLE LIE ALGEBRAS; 13.1. Enveloping algebras of Lie algebras; 13.2. Poincar�e-Birkhoff-Witt theorem; 13.3. Applications to representations of semisimple Lie algebras; CHAPTER 14. CHARACTERS OF IRREDUCIBLE REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS.