Clifford Algebras and the Classical Groups

Clifford Algebras and the Classical Groups

by Ian R. Porteous
     
 

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the… See more details below

Overview

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G[subscript 2], and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

Product Details

ISBN-13:
9780521118026
Publisher:
Cambridge University Press
Publication date:
08/06/2009
Series:
Cambridge Studies in Advanced Mathematics Series, #50
Pages:
308
Product dimensions:
5.90(w) x 9.00(h) x 0.50(d)

Table of Contents

Foreword
1Linear spaces1
2Real and complex algebras9
3Exact sequences18
4Real quadratic spaces22
5The classification of real quadratic spaces32
6Anti-involutions of R(n)43
7Anti-involutions of C(n)49
8Quaternions57
9Quaternionic linear spaces67
10Anti-involutions of H(n)72
11Tensor products of algebras81
12Anti-involutions of [superscript 2]K(n)91
13The classical groups100
14Quadric Grassmannians110
15Clifford algebras123
16Spin groups140
17Conjugation148
182 x 2 Clifford matrices167
19The Cayley algebra178
20Topological spaces191
21Manifolds202
22Lie groups225
23Conformal groups245
24Triality256
References285
Index289

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >