Lie groups and compact groups / John F. Price.

Includes bibliographical references (pages 169-173) and index.

Print version record.

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.

Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups

4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups

A. 4 The Haar integralBibliography; Index

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