An introduction to the spinorial chessboard
type: Item
instance of: scholarly article
title: An introduction to the spinorial chessboard
zbMATH Open document ID: 0657.15021
DOI: 10.1016/0393-0440(87)90019-2
author: P. Budinich
author: Andrzej Trautman
published in: Journal of Geometry and Physics
publication date: 1987-01-01T00:00:00Z
review text: With the applications of higher-dimensional spinors to physics in mind, the authors give an account of the real Clifford algebras. Let Cl(k,\(\ell)\) denote the Clifford algebra associated with a real scalar product of signature (k,\(\ell)\). The spinorial chessboard of the title is made up of the 64 such algebras with \(0\leq k,\ell \leq 7\). Certain periodicities relate the properties of the general Cl(k,\(\ell)\) to those on the chessboard. For example, its type and the kind of symmetry of its invariant bilinear form depend only on the respective values of k-\(\ell\) and \(k+\ell\) modulo 8. The inductive construction of a set of Dirac matrices, and of other related matrices, are discussed in some detail. The present article is intended as an introduction to a more detailed account of the spinorial chessboard.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 4073198
zbMATH Keywords: spinors
zbMATH Keywords: real Clifford algebras
zbMATH Keywords: spinorial chessboard
zbMATH Keywords: symmetry
zbMATH Keywords: invariant bilinear form
zbMATH Keywords: Dirac matrices
reviewed by: G. E. Wall
MaRDI profile type: Publication
full work available at URL: 0393-0440(87)90019-2
OpenAlex ID: W2008098610
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description: scientific article; zbMATH DE number 4073198