Lie groups and compact groups / John F. Price.

Format:

Book

Author/Creator:

Price, John F. (John Frederick), 1943- author.

Series:

London Mathematical Society lecture note series ; 25.

London Mathematical Society lecture note series ; 25

Language:

English

Subjects (All):

Lie groups.

Compact groups.

Physical Description:

1 online resource (ix, 177 pages) : digital, PDF file(s).

Other Title:

Lie Groups & Compact Groups

Place of Publication:

Cambridge : Cambridge University Press, 1977.

Language Note:

English

Summary:

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.

Contents:

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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88371-2

1-107-36577-5

1-107-37050-7

1-107-36086-2

1-107-36869-3

1-299-40358-1

1-107-36331-4

0-511-60071-2