Idempotents of Clifford Algebras

TL;DR

This paper classifies idempotents in Clifford algebras C(p,q), showing they form continuous families via matrix ring isomorphisms, including primitive idempotents for minimal ideals, with examples in low dimensions.

Contribution

It provides a comprehensive classification of idempotents in Clifford algebras using isomorphisms to matrix rings, revealing continuous families and primitive idempotents.

Findings

Idempotents in Clifford algebras form continuous families.

Primitive idempotents generate minimal one-sided ideals.

Classification includes low-dimensional examples.

Abstract

A classification of idempotents in Clifford algebras C(p,q) is presented. It is shown that using isomorphisms between Clifford algebras C(p,q) and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive idempotents used to generate minimal one sided ideals in Clifford algebras. Some low dimensional examples are discussed.