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Lie groups and compact groups /
The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon res...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1977.
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| Colección: | London Mathematical Society lecture note series ;
25. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups
- 4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups
- A. 4 The Haar integralBibliography; Index