Idempotent structure of Clifford algebras
type: Item
instance of: scholarly article
title: Idempotent structure of Clifford algebras
zbMATH Open document ID: 0658.15030
DOI: 10.1007/BF00047537
author: Pertti Lounesto
author: G. P. Wene
published in: Acta Applicandae Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: Spinor spaces can be represented as minimal left ideals of Clifford algebras and they are generated by primitive idempotents. Primitive idempotents of the Clifford algebras \({\mathbb{R}}_{p,q}\) are shown to be products of mutually nonannihilating commuting idempotent factors \(1/2(1+e_ T)\), where the \(k=q-r_{q-p}\) basis elements \(e_ T\) satisfy \(e^ 2_ T=1\). The lattice generated by a set of mutually annihilating primitive idempotents is examined. The final result characterizes all Clifford algebras \(R_{p,q}\) with an anti-involution such that each symmetric element is either a nilpotent or then some right multiple of it is a nonzero symmetric idempotent. This happens when \(p+q\leq 3\) and (p,q)\(\neq (2,1)\).
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 4075302
zbMATH Keywords: Spinor spaces
zbMATH Keywords: minimal left ideals
zbMATH Keywords: Clifford algebras
zbMATH Keywords: primitive idempotents
zbMATH Keywords: anti-involution
MaRDI profile type: Publication
cites work: Perturbation theory of Kepler motion based on spinor regularization.
cites work: Development of spinor descriptions of rotational mechanics from Euler's rigid body displacement theorem
cites work: First order elliptic systems. A function theoretic approach
cites work: The fifteen-parameter conformal group
cites work: The Clifford algebra of differential forms
cites work: A general method of generating and classifying Clifford algebras
cites work: The Dirac equation in exterior form
cites work: Q5579608
cites work: Q5777227
cites work: Q3236717
cites work: Q5519166
cites work: Q5830680
cites work: Jordan and associative rings with nilpotent and invertible elements
cites work: On a Result of Osborn
cites work: Alternative rings whose symmetric elements are nilpotent or a right multiple is a symmetric idempotent
full work available at URL: https://doi.org/10.1007/bf00047537
OpenAlex ID: W2084633397
description: scientific article; zbMATH DE number 4075302