Lectures on Lie Groups and Lie Algebras,9780521495790

Lectures on Lie Groups and Lie Algebras

by
ISBN13: 9780521495790
ISBN10: 0521495792
Format: Hardcover
Pub. Date: 1995-09-29
Publisher(s): Cambridge University Press
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Summary

Three of the leading figures in the field have composed this excellent introduction to the theory of Lie groups and Lie algebras. Together these lectures provide an elementary account of the theory that is unsurpassed. In the first part, Roger Carter concentrates on Lie algebras and root systems. In the second Graeme Segal discusses Lie groups. And in the final part, Ian Macdonald gives an introduction to special linear groups. Graduate students requiring an introduction to the theory of Lie groups and their applications should look no further than this book.

Table of Contents

Foreword vii
M. J. Taylor
Lie Algebras and Root Systems 1(44)
R. W. Carter
Preface
3(2)
Introduction to Lie algebras
5(7)
Basic concepts
5(2)
Representations and modules
7(1)
Special kinds of Lie algebra
8(2)
The Lie algebras sln (C)
10(2)
Simple Lie algebras over C
12(13)
Cartan subalgebras
12(1)
The Cartan decomposition
13(2)
The Killing form
15(1)
The Weyl group
16(2)
The Dynkin diagram
18(7)
Representations of simple Lie algebras
25(11)
The universal enveloping algebra
25(1)
Verma modules
26(1)
Finite dimensional irreducible modules
27(2)
Weyl's character and dimension formulae
29(3)
Fundamental representations
32(4)
Simple groups of Lie type
36(9)
A Chevalley basis of g
36(2)
Chevalley groups over an arbitrary field
38(1)
Finite Chevalley groups
39(2)
Twisted groups
41(2)
Suzuki and Ree groups
43(1)
Classification of finite simple groups
44(1)
Lie Groups 45(88)
Graeme Segal
Introduction
47(2)
Examples
49(4)
SU2, SO3, and SL2R
53(6)
Homogeneous spaces
59(4)
Some theorems about matrices
63(6)
Lie theory
69(13)
Representation theory
82(3)
Compact groups and integration
85(4)
Maximal compact subgroups
89(2)
The Peter-Weyl theorem
91(9)
Functions on Rn'' and Sn-1
100(4)
Induced representations
104(4)
The complexification of a compact group
108(2)
The unitary and symmetric groups
110(5)
The Borel-Weil theorem
115(5)
Representations of non-compact groups
120(4)
Representations of SL2R
124(4)
The Heisenberg group
128(5)
Linear Algebraic Groups 133(53)
I.G. Macdonald
Preface
135(2)
Introduction
137(2)
Affine algebraic varieties
139(7)
Linear algebraic groups: definition and elementary properties
146(11)
Interlude
154(3)
Projective algebraic varieties
157(5)
Tangent spaces. Separability
162(4)
The Lie algebra of a linear algebraic group
166(6)
Homogeneous spaces and quotients
172(5)
Borel subgroups and maximal tori
177(5)
The root structure of a linear algebraic group
182(4)
Notes and references 186(1)
Bibliography 187(2)
Index 189

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