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An Introduction to Clifford Algebras and Spinors$
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Jayme Vaz, Jr. and Roldão da Rocha, Jr.

Print publication date: 2016

Print ISBN-13: 9780198782926

Published to Oxford Scholarship Online: August 2016

DOI: 10.1093/acprof:oso/9780198782926.001.0001

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Classification and Representation of the Clifford Algebras

Classification and Representation of the Clifford Algebras

Chapter:
(p.87) 4 Classification and Representation of the Clifford Algebras
Source:
An Introduction to Clifford Algebras and Spinors
Author(s):

Jayme Vaz

Roldão da Rocha

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198782926.003.0004

In this chapter, the classification and representation of Clifford algebras are introduced and discussed. Some important theorems regarding the structure of Clifford algebras are presented; later on, these are used for the classification and construction of the representations of the Clifford algebras as well. The periodicity theorems and their generalisation are demonstrated and exemplified. The Clifford algebras up to dimension 8 in all metric signatures are explicitly derived; hence, with the aid of the periodicity theorem, all Clifford algebras of finite dimension are classified. In addition, procedures to explicitly build Clifford algebra matrix representations are presented, through the idempotent structure.

Keywords:   Clifford Algebra, periodicity theorem, representation, idempotent, algebra

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