Abstract Lie algebras/ David J. Winter.

Preface; 1.1 Introduction; 1.2 Complete Reducibility; 1.3 Ascent and Descent; 1.4 Jordan Decomposition; 1.5 Fitting Decomposition; 1 Modules; 2.1 Introduction; 2.2 Ascent and Descent; 2.3 Translations and the Multiplication Algebra; 2.4 Derivations; 2.5 Solvability; the Radical of u; 2.6 Simplicity and Semisimplicity; 2.7 Nonassociative Algebras with Invariant Forms; 2.8 Lie Algebras with Invariant Forms; 2 Nonassociative Algebras; 3.1 Introduction; 3.2 Nilpotent Lie Algebras; Engel's Theorem; 3.3 Cartan Subalgebras; 3.4 Solvable Lie Algebras. 3.5 Cartan's Criteria3.6 Existence of Complements; 3.7 Classification of Split Semisimple Lie Algebras; 3.8 Automorphisms; Conjugacy Theorems; 3 Lie Algebras of Characteristic 0; 4.1 Introduction; 4.2 A-graded Lie Algebras; 4.3 Nilpotent Lie Algebras; 4.4 Cartan Subalgebras; 4.5 The Toral Structure of a Lie p-Algebra; 4.6 Exponentials; 4 Lie Algebras of Arbitrary Characteristic; Appendix The Zariski Topology; References; Index.