Division algebras, Clifford algebras, periodicity
type: Item
instance of: scholarly article
title: Division algebras, Clifford algebras, periodicity
zbMATH Open document ID: 1393.15031
author: Geoffrey Dixon
published in: Advances in Applied Clifford Algebras
publication date: 2018-06-21T00:00:00Z
review text: Periodicities in Clifford algebra theory of orders \(2,4,\) and \(8\) are well known. Starting from a result from lattice theory, in which a \(24\)-dimensional Leech lattice can be represented in the \(3\)-dimensional space with octonion components, the main goal of this paper is to prove that, by exploiting the octonion algebra, in Clifford algebra representation theory a periodicity of order 24 arises.
reviewed by: Cristina Flaut
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 17A35
Mathematics Subject Classification ID: 16K20
zbMATH DE Number: 6892833
zbMATH Keywords: division algebra
zbMATH Keywords: Clifford algebra
MaRDI profile type: Publication
full work available at URL: s00006-018-0820-8
OpenAlex ID: W2793362879
cites work: A Conceptual Breakthrough in Sphere Packing
cites work: Lattices with few distances
cites work: Q4303985
cites work: Q5496722
cites work: Q3890822
cites work: The sphere packing problem in dimension 8
cites work: Octonions and the Leech lattice
DOI: 10.1007/S00006-018-0820-8
description: scientific article; zbMATH DE number 6892833