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Representations of Lie algebras : an introduction through gln /
"This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules o...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
|
| Colección: | Australian Mathematical Society lecture series ;
22. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises.
- CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules.
- 7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index.