Table of Contents

Chapter VII - Cartan Subalgebras and Regular Elements: Primary Decomposition of Linear Representations.- Cartan Subalgebras and Regular Elements of a Lie Algebra.- Conjugacy Theorems.- Regular Elements of a Lie Group.- Decomposable Linear Lie Algebras.- Chapter VIII - Split Semi-Simple Lie Algebras: Root System of a Split Semi-Simple Lie Algebra.- Subalgebras of Split Semi-Simple Lie Algebras.- Automorphisms of a Semi-Simple Lie Algebra.- Modules over a Split Semi-Simple Lie Algebra.- Finite Dimensional Modules over a Split Semi-simple Lie.- Symmetric Invariants.- The Formula of Hermann Weyl.- Maximal Subalgebras.- Chevalley Orders.- Classical Splittable Simple Lie Algebras.- Chapter IX - Compact Real Lie Groups: Compact Lie Algebras.- Maximal Tori of Compact Lie Groups.- Compact Forms of Complex Semi-Simple Lie Algebras.- Root System Associated to a Compact Group. Conjugacy Classes. Integration on Compact Lie Groups.- Irreducible Representations of connected compact Lie Groups.- Fourier Transform.- Compact Lie Groups Operating on Manifolds.- Appendices.