Author(s): Melvin Hausner, Jacob T. Schwartz
Publisher: Nelson
Year: 1968
Title page
Preface
Section 0
A. Algebra
B. Functions of Operators
C. Analysis
D. Topology
E. Topological Groups
Part I. Lie Groups and Their Lie Algebras
1. Manifolds
2. Lie Groups: Local and Global Properties
3. The Lie Algebra
4. The Exponential Function
5. The Campbell-Baker-Hausdorff Theorem
6. Subgroups and Sub-algebras
7. Important examples - the classical matrix groups
Part II. Complex Semi-Simple Lie Algebras
1. Basics
2. Cartan's Criterion
3. Structure of Simple Complex Algebras
4. Models of the Simple Complex Algebras
5. Isomorphisms and Automorphisms
6. Representations of Complex Semi-Simple Algebras
7. The radical splitting theorem. Existence of Lie Groups with a given Lie algebra
Part III. Real Semi-Simple Lie Algebras
1. Structure and Representations of Simple Real Algebras
A. Analysis of the conjugations in the Lie Algebra of type A_{n-l}
B. Analysis of the conjugations in the Lie Algebra of types B_m, C_m and D_m
A'. Analysis of the conjugations in the Lie Algebra of type G₂
B'. Analysis of the conjugations in the Lie Algebra of type E₈
C'. Analysis of the conjugations in the Lie Algebra of type E₇
D'. Analysis of the conjugations in the Lie Algebra of type E₆
E'. Analysis of the conjugations in the Lie Algebra of type F₄
2. Compact Connected Lie Groups
Index
