Clifford ${mathcal{A}}$ -algebras of Quadratic ${mathcal{A}}$ -Modules

摘要

A Clifford ${mathcal{A}}$ -algebra of a quadratic ${mathcal{A}}$ -module ( ${mathcal{E}}$ , q) is an associative and unital ${mathcal{A}}$ -algebra (i.e. sheaf of ${mathcal{A}}$ -algebras) associated with the quadratic ${mathcal{S}}$ h ${mathcal{S}}$ et X -morphism q, and satisfying a certain universal property. By introducing sheaves of sets of orthogonal bases (or simply sheaves of orthogonal bases), we show that with every Riemannian quadratic free ${mathcal{A}}$ -module of finite rank, say, n, one can associate a Clifford free ${mathcal{A}}$ -algebra of rank 2 n . This “main” result is stated in Theorem 3.2.