دانلود کتاب Introduction to Lie algebras and representation theory

فهرست مطالب :

PREFACE
I. BASIC CONCEPTS
1. Definitions and first examples
1.1 The notion of Lie algebra
1.2 Linear Lie algebras
1.3 Lie algebras of derivations
1.4 Abstract Lie algebras
2. Ideals and homomorphisms
2.1 Ideals
2.2 Homomorphisms and representations
2.3 Automorphisms
3. Solvable and nilpotent Lie algebras
3.1 Solvability
3.2 Nilpotency
3.3 Proof of Engel\'s Theorem 1
II. SEMISIMPLE LIE ALGEBRAS
4. Theorems of Lie and Cartan
4.1 Lie\'s Theorem
4.2 Jordan-Chevalley decomposition
4.3 Cartan\'s Criterion
5. Killing form
5.1 Criterion for semi simplicity
5.2 Simple ideals of L
5.3 Inner derivations
5.4 Abstract Jordan decomposition
6. Complete reducibility of representations
6.1 Modules
6.2 Casimir element of a representation
6.3 Weyl\'s Theorem
6.4 Preservation of Jordan decomposition
7. Representations of