Clifford \({\mathcal{A}}\)-algebras of quadratic \({\mathcal{A}}\)-modules
type: Item
instance of: scholarly article
title: Clifford \({\mathcal{A}}\)-algebras of quadratic \({\mathcal{A}}\)-modules
zbMATH Open document ID: 1269.15025
author: Patrice Ntumba
published in: Advances in Applied Clifford Algebras
publication date: 2012-11-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 6111307
zbMATH Keywords: Clifford \(\mathcal{A}\)-morphism
zbMATH Keywords: quadratic \(\mathcal{A}\)-morphism
zbMATH Keywords: Riemannian quadratic \(\mathcal{A}\)-module
zbMATH Keywords: Clifford \(\mathcal{A}\)-algebra
zbMATH Keywords: principal \({\mathcal{A}}\)-automorphism
zbMATH Keywords: evensub-\({\mathcal{A}}\)-algebra
zbMATH Keywords: \({\mathcal{A}}\)-antiautomorphism
zbMATH Keywords: sub-\({\mathcal{A}}\)-module of odd products
MaRDI profile type: Publication
full work available at URL: s00006-012-0333-9
OpenAlex ID: W1998555395
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DOI: 10.1007/S00006-012-0333-9
description: scientific article; zbMATH DE number 6111307