Intro; Preface; Contents; About the Authors; Introduction; 1 Preliminaries; 1.1 Commutative Algebra; 1.2 Affine Varieties; 1.3 Projective Varieties; 1.4 Schemes
Affine and Projective; 1.5 The Scheme Spec(A); 1.6 The Scheme Proj(S); 1.7 Sheaves of OX-Modules; 1.8 Attributes of Varieties; 2 Structure Theory of Semisimple Rings; 2.1 Semisimple Modules; 2.2 Semisimple Rings; 2.3 Brauer Groups and Central Simple Algebras; 2.4 The Group Algebra, K[G]; 2.5 The Center of K[G]; Exercises; 3 Representation Theory of Finite Groups; 3.1 Representations of G; 3.2 Characters of Representations

6 Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C)6.1 Generalities; 6.2 Schur-Weyl Duality; 6.3 Characters of the Schur Modules; 6.4 Schur Module Representations of SLn (C); 6.5 Representations of GLn (C); Exercises; 7 Structure Theory of Complex Semisimple Lie Algebras; 7.1 Introduction to Semisimple Lie Algebras; 7.2 The Exponential Map in Characteristic Zero; 7.3 Structure of Semisimple Lie Algebras; 7.4 Jordan Decomposition in Semisimple Lie Algebras; 7.5 The Lie Algebra sln (C); 7.6 Cartan Subalgebras; 7.7 Root Systems; 7.8 Structure Theory of sln (C)

Exercises8 Representation Theory of Complex Semisimple Lie Algebras; 8.1 Representations of g; 8.2 Weight Spaces; 8.3 Finite Dimensional Modules; 8.4 Fundamental Weights; 8.5 Dimension and Character Formulas; 8.6 Irreducible sln (C)-Modules; Exercises; 9 Generalities on Algebraic Groups; 9.1 Algebraic Groups and Their Lie Algebras; 9.2 The Tangent Space; 9.3 Jordan Decomposition in G; 9.4 Variety Structure on G/H; 9.5 The Flag Variety; 9.6 Structure of Connected Solvable Groups; 9.7 Borel Fixed Point Theorem; 9.8 Variety of Borel Subgroups; Exercises; 10 Structure Theory of Reductive Groups