Clifford \({\mathcal{A}}\)-algebras of quadratic \({\mathcal{A}}\)-modules
Let \(\mathcal{A}\) be a sheaf of unital and commutative algebras over a topological space \(X\). Let \(\mathcal{E}\) be a free \(\mathcal{A}\)-module of finite rank, \(q\) a quadratic \(\text{SETS}\)-morphism, sending the sheaf of sets of \(\mathcal{E}\) into the sheaf of sets of \(\mathcal{A}\), and a Riemannian quadratic free \(\mathcal{A}\)-module \((\mathcal{E},q)\) of finite rank, that is, a quadratic free \(\mathcal{A}\)-module such that the \(q\)-induced \(\mathcal{A}\)-bilinear morphism is a Riemannian \(\mathcal{A}\)-metric. The objective of this paper is to prove that, with every Riemannian quadratic free \(\mathcal{A}\)-module of finite rank \(n\), up to \(\mathcal{A}\)-isomorphism, a Clifford free \(\mathcal{A}\)-algebra of rank \(2^n\) is associated.
Riemannian quadratic \(\mathcal{A}\)-module
principal \({\mathcal{A}}\)-automorphism
sub-\({\mathcal{A}}\)-module of odd products
scientific article; zbMATH DE number 6111307