NONCOMPACT SEMISIMPLE LIE GROUPS

Abstract

CONTENTS Foreword Chapter I. Introduction § 1. Linear Lie groups § 2. Semisimple Lie groups § 3. Symmetric riemannian spaces Chapter II. The fundamental theorems § 4. Statement of the fundamental theorems § 5. Proof of the algebra decomposition theorem § 6. Properties of the Cartan decomposition of a simple algebra § 7. Proof of the decomposition theorem for groups with trivial centre § 8. The symmetric riemannian space . Proof of the conjugacy theorem for groups with trivial centre § 9. The general case Chapter III. The centres of the noncompact real semisimple Lie groups and the kernels of their linear representations § 10. Introductory material § 11. The canonical form of an involutory automorphism and the enumeration of the real forms of the complex simple algebras § 12. The centre of a real semisimple group § 13. Formulae for the centres of the simply-connected non-compact simple Lie groups § 14. Another method of finding the centres § 15. Linear real semisimple groups § 16. Linearizers and kernels of linear representations § 17. Formulae for linearizers and kernels of linear representations References