Lie Groups and Compact Groups

John F. Price

doi:10.1017/CBO9780511600715

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.

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Lie Groups and Compact Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-x

Chapter 1 - Analytic manifolds
pp 1-23

Chapter 2 - Lie groups and Lie algebras
pp 24-57

Chapter 3 - The Campbell-Baker-Hausdorff formula
pp 58-78

Chapter 4 - The geometry of Lie groups
pp 79-100

Chapter 5 - Lie subgroups and subalgebras
pp 101-114

Chapter 6 - Characterisations and structure of compact Lie groups
pp 115-159

Appendix A - Abstract harmonic analysis
pp 160-168

Biblography
pp 169-173

Index
pp 174-177

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