Factorization of Lipschitzian elements
type: Item
instance of: scholarly article
title: Factorization of Lipschitzian elements
zbMATH Open document ID: 1307.15031
author: Jacques Helmstetter
published in: Advances in Applied Clifford Algebras
publication date: 2014-12-15T00:00:00Z
review text: Let \(V\) be a vector space over a field \(K\) and let \(q: V\rightarrow K\) be a quadratic form. Denote as \(\mathrm{Cl}(V,q)\) the corresponding Clifford algebra. The Lipschitz monoid \(\mathrm{Lip}(V,q)\) is the multiplicative monoid generated in \(\mathrm{Cl}(V,q)\) by all scalars in \(K\), all vectors in \(V\) and elements \(1+xy\), where \(x\) and \(y\) are vectors that span a totally isotropic plane. The main results of the paper are the following. It is proved that if \(K\) contains at least three scalars, then every element \(a\in \mathrm{Lip}(V,q)\) such that \(\mathrm{Supp}(a)\) is not totally isotropic can be expressed as follows: \(a=x_1\dots x_s\), where \(x_1\),\dots, \(x_s\) form a base of \(\mathrm{Supp}(a)\). An algorithm of the construction of such a decomposition is proposed.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 20M32
zbMATH DE Number: 6380694
zbMATH Keywords: Clifford algebras
zbMATH Keywords: Lipschitz monoids
zbMATH Keywords: quadratic form
zbMATH Keywords: algorithm
reviewed by: Dmitry Artamonov
MaRDI profile type: Publication
full work available at URL: s00006-014-0467-z
OpenAlex ID: W2085337197
cites work: A survey of Lipschitz monoids
cites work: Q5830680
cites work: Q5795141
cites work: Q4132666
cites work: Lipschitz monoids and Vahlen matrices
cites work: Lipschitzian subspaces in Clifford algebras
cites work: Q5592339
cites work: Q5421346
cites work: Q3997794
cites work: Holonomic quantum fields. I
DOI: 10.1007/S00006-014-0467-Z
description: scientific article; zbMATH DE number 6380694