Explicit isomorphisms of real Clifford algebras

Abstract

It is well known that the Clifford algebra Clp,q associated to a nondegenerate quadratic form on ℝn (n=p+q) is isomorphic to a matrix algebra K(m) or direct sum K(m)⊕K(m) of matrix algebras, where K=ℝ,ℂ,ℍ. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms.