Classification of Clifford Algebras - Notation and Conventions

Notation and Conventions

The Clifford product is the manifest ring product for the Clifford algebra, and all algebra homomorphisms in this article are with respect to this ring product. Other products defined within Clifford algebras, such as the exterior product, are not used here. This article uses the (+) sign convention for Clifford multiplication so that

for all vectors v ∈ V, where Q is the quadratic form on the vector space V. We will denote the algebra of n×n matrices with entries in the division algebra K by K(n). The direct sum of two such identical algebras will be denoted by K2(n) = K(n) ⊕ K(n).