Irreducible Clifford modules.
type: Item
instance of: scholarly article
title: Irreducible Clifford modules.
zbMATH Open document ID: 1042.15015
published in: Tsukuba Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: Let \(C\ell_n\) be the complex Clifford algebra on \(\mathbb{C}^n\), and let \(\Delta_{2n}\) be the irreducible \(C\ell_{2n}\)-module. The author uses the bimodule isomorphism \(C\ell_{2n}\cong \Delta\times \Delta\) to derive matrix representations of \(C\ell_{2n}\) and hence to exhibit a list of generators of the irreducible modules over \(C\ell_n\), for all \(n\). The algebra \(C\ell_s\) is examined in detail, and a relationship between Clifford algebras and the octonions is presented.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 1998404
zbMATH Keywords: Clifford algebra
zbMATH Keywords: matrix algebra
zbMATH Keywords: spinor space
zbMATH Keywords: Lie group
zbMATH Keywords: matrix representations
zbMATH Keywords: irreducible modules
zbMATH Keywords: octonions
author: Jianwei Zhou
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164560
OpenAlex ID: W1489219260
DOI: 10.21099/TKBJM/1496164560
description: scientific article; zbMATH DE number 1998404