Synopses & Reviews
The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups.
Provides a self-contained introduction to Lie groups and makes results about the structure of Lie groups and compact groups available to a wide audience.
Table of Contents
1. Analytic manifolds; 2. Lie groups and Lie algebras; 3. The Campbell-Baker-Hausdorff formula; 4. The geometry of Lie groups; 5 Lie subgroups and subalgebras; 6. Characterizations and structure of compact Lie groups.