ABSTRACT

This book provides an account of part of the theory of Lie algebras most relevant to Lie groups. It discusses the basic theory of Lie algebras, including the classification of complex semisimple Lie algebras, and the Levi, Cartan and Iwasawa decompositions.

chapter Chapter 1|70 pages

General Theory of Lie Algebras

chapter Chapter 2|64 pages

Semisimple Lie Algebras

chapter Chapter 3|26 pages

Cohomology of Lie Algebras and its Application

chapter Chapter 4|35 pages

Semisimple Lie Algebras Over ℝ and ℂ

chapter Chapter 5|52 pages

Groups Connected with a Root System

chapter Chapter 6|67 pages

Linear Groups

chapter Chapter 7|71 pages

Irreducible Representations

chapter Chapter 8|57 pages

Classification of Real Simple Lie Algebras