Spinor modules of Clifford algebras in classes \(N_{2k-1}\) and \(\Omega _{2k-1}\) are determined by irreducible nonlinear characters of corresponding Salingaros vee groups
type: Item
instance of: scholarly article
title: Spinor modules of Clifford algebras in classes \(N_{2k-1}\) and \(\Omega _{2k-1}\) are determined by irreducible nonlinear characters of corresponding Salingaros vee groups
zbMATH Open document ID: 1395.15017
author: Rafał Abłamowicz
published in: Advances in Applied Clifford Algebras
publication date: 2018-08-15T00:00:00Z
review text: The goal of this paper is to prove that for any \(k \in \{1,2,3,4\}\) and any Salingaros vee group \(G_{p,q}\) in classes \(N_{2k-1}\) or \(\Omega_{2k-1}\), each character of \(G_{p,q}\) can be realized over \(\mathbb{R}\). As a result, every nonlinear character of \(G_{p,q}\) uniquely determines a spinor module of \(C\ell_{p,q}\) which is faithful for classes \(N_{2k-1}\) and unfaithful for classes \(\Omega_{2k-1}\). This generalizes a known fact on the isomorphic Clifford algebras \(C\ell_{2,0}\) and \(C\ell_{1,1}\), whose Salingaros vee groups belong to the class \(N_1\).
reviewed by: Adam Chapman
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 6918635
zbMATH Keywords: Salingaros vee group
zbMATH Keywords: spinor module
zbMATH Keywords: group rings
describes a project that uses: CLIFFORD
describes a project that uses: SymGroupAlgebra
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s00006-018-0867-6
OpenAlex ID: W2800676199
cites work: A classification of Clifford algebras as images of group algebras of Salingaros vee groups
cites work: Mathematics of Clifford -- a Maple package for Clifford and Graßmann algebras
cites work: Using periodicity theorems for computations in higher dimensional Clifford algebras
cites work: Q5634146
cites work: Q3140236
cites work: Q4544915
cites work: Clifford algebras and spinors.
cites work: Q5267575
cites work: Q4540930
cites work: Realization, extension, and classification of certain physically important groups and algebras
cites work: On the classification of Clifford algebras and their relation to spinors in n dimensions
cites work: The relationship between finite groups and Clifford algebras
DOI: 10.1007/S00006-018-0867-6
description: scientific article; zbMATH DE number 6918635