A note on pseudo-reflections
type: Item
instance of: scholarly article
title: A note on pseudo-reflections
zbMATH Open document ID: 0626.15003
DOI: 10.1016/S0195-6698(87)80005-7
author: Ofer Gabber
published in: European Journal of Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: Let V be a finite dimensional vector space and G a group of automorphisms of V generated by pseudo-reflections, i.e. linear transformations \(T: V\to V\) satisfying \(rank(T-id_ V)=1\). Suppose V carries a nondegenerate bilinear form invariant under G. The author shows that if the elements of G have no common fixed vector, then for every linear transformation \(T: V\to V\), there exists \(g\in G\) such that g-T is invertible.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4017094
zbMATH Keywords: pseudo-reflections
zbMATH Keywords: common fixed vector
reviewed by: Paul Yiu
MaRDI profile type: Publication
cites work: Q5580319
cites work: Q5588717
description: scientific article; zbMATH DE number 4017094