Quaternion types of Clifford algebra elements, basis-free approach

Abstract

We consider Clifford algebras over the field of real or complex numbers as a quotient algebra without fixed basis. We present classification of Clifford algebra elements based on the notion of quaternion type. This classification allows us to reveal and prove a number of new properties of Clifford algebras. We rely on the operations of conjugation to introduce the notion of quaternion type. Also we find relations between the concepts of quaternion type and rank of Clifford algebra element.

Proceedings 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Weimar, July 15-20, 2011

References in corpus (1)

• Unitary spaces on Clifford algebras

Cited by in corpus (1)

• Clifford algebras and their applications to Lie groups and spinors