This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author includes an exhaustive treatment of all the generalizations of the classical groups, as well as an excellent exposition of the classification of the conjugation anti-involution of the Clifford algebras and their complexifications. Toward the end of the book, the author introduces ideas from the theory of Lie groups and Lie algebras. This treatment of Clifford algebras will be welcomed by graduate students and researchers in algebra.
Author(s): I. Porteous
Series: Cambridge Studies in Advanced Mathematics 50
Publisher: Cambridge University Press
Year: 1995
Language: English
Pages: 308
Contents......Page 8
Foreword......Page 10
1 Linear spaces......Page 12
2 Real and complex algebras......Page 20
3 Exact sequences......Page 29
4 Real quadratic spaces......Page 33
5 The classification of real quadratic spaces......Page 43
6 Anti-involutions of R(n)......Page 54
7 Anti-involutions of C(n)......Page 60
8 Quaternions......Page 68
9 Quaternionic linear spaces......Page 78
10 Anti-involutions of H(n)......Page 83
11 Tensor products of algebras......Page 92
12 Anti-involutions of 2K(n)......Page 102
13 The classical groups......Page 111
14 Quadric Grassmannians......Page 121
15 Clifford algebras......Page 134
16 Spin groups......Page 151
17 Conjugation......Page 159
18 2 x 2 Clifford matrices......Page 178
19 The Cayley algebra......Page 189
20 Topological spaces......Page 202
21 Manifolds......Page 213
22 Lie groups......Page 236
23 Conformal groups......Page 256
24 Triality......Page 267
References......Page 296
Index......Page 300
