Chain spaces with many reflections
type: Item
instance of: scholarly article
title: Chain spaces with many reflections
zbMATH Open document ID: 1001.51007
author: Andrea Blunck
published in: Journal of Geometry
publication date: 2002-12-09T00:00:00Z
review text: Let \(\Sigma=({\mathbf P},{\mathcal C})\) be a chain space, where \({\mathbf P}\) is a set of points and \({\mathcal C}\) is a set of chains. Let \(\Pi\) be a subgroup of the automorphism group \(\text{ Aut} \Sigma\) and let \(I\) be a distinguished set of involutions in \(\Pi;\) the elements in \(I\) are called reflections. The author gives axioms for chain spaces, one of the axioms is the three-reflection theorem. She obtains coordinatizations for certain chain spaces with reflections, i.e., she determines \(\Pi',\) \(K,\) \(R\) such that \((\Pi,\Sigma)\cong(\Pi',\Sigma(K,R)),\) where \(K\) is a field, \(R\) is a commutative stable \(K\)-algebra, and \(\Pi'\leq PGL_2(R).\)
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 51B05
zbMATH DE Number: 1760622
zbMATH Keywords: chain space
zbMATH Keywords: chain geometry
zbMATH Keywords: involution
zbMATH Keywords: three-reflection theorem
zbMATH Keywords: coordinatization
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: s00022-001-8566-0
OpenAlex ID: W1981973671
DOI: 10.1007/S00022-001-8566-0
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description: scientific article; zbMATH DE number 1760622