The Clifford algebra of an infinite-dimensional space

Abstract

The Clifford algebra of a real infinite-dimensional vector space is constructed. This algebra contains all finite- and infinite-dimensional Clifford algebras over the real and complex numbers. Some of the mathematical properties of these algebras are discussed; the automorphisms and involutions are specifically addressed. The special case with metric gνμ=δνμ, ν, μ=1,2,..., follows as a corollary to the more general results.