Orthogonal Cayley-Klein groups
type: Item
instance of: scholarly article
title: Orthogonal Cayley-Klein groups
zbMATH Open document ID: 1124.51006
DOI: 10.1007/BF03322905
author: Rolf Struve
published in: Results in Mathematics
publication date: 2006-03-07T00:00:00Z
review text: The author calls the following setting a Cayley-Klein vector space. In a finite-dimensional vector space \(V\neq\{0\}\) over a field of characteristic \(\neq 2\) let \(V= R_0\supset R_1\supset\cdots\supset R_r= \{0\}\) be a proper chain of subspaces and \(f_1,\dots, f_r\) symmetric bilinear forms such that \(f_i: R_{i-1}\times R_{i-1}\to K\) and \(\text{rad\,}f_i= R_i\) for \(i= 1,\dots,r\). Vectors \(a,b\in V\) are called orthogonal if \(a,b\in R_{i-1}\) implies that \(f_i(a, b)= 0\) for \(i= 1,\dots, r\). In the group of automorphisms of a Cayley-Klein vector space each automorphism is a product of involutions with one-dimensional negative spaces. This corresponds to the fact that each element of an orthogonal group is a product of symmetries.
Mathematics Subject Classification ID: 51F25
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 5009763
zbMATH Keywords: vector spaces
zbMATH Keywords: orthogonal groups
zbMATH Keywords: reflection groups
zbMATH Keywords: polarities
zbMATH Keywords: projective metric
zbMATH Keywords: Cayley-Klein geometry
zbMATH Keywords: geometric algebra
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322905
OpenAlex ID: W2069676832
description: scientific article; zbMATH DE number 5009763