Clifford A-algebras of quadratic A-modules

Abstract

A Clifford A-algebra of a quadratic A-module (E, q) is an associative and unital A-algebra (i.e. sheaf of A-algebras) associated with the quadratic ShSetX-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 A-module of finite rank, say, n, one can associate a Clifford free A-algebra of rank 2n. This “main” result is stated in Theorem 3.2.