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

Abstract

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\({\mathcal{S}}\)etX-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 2n. This “main” result is stated in Theorem 3.2.