Idempotents of Clifford Algebras

A classification of idempotents of Clifford algebras Cp,q is presented. It is shown that using isomorphisms between Clifford algebras Cp,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.