Products of involutions in \(O^ +(V)\)
type: Item
instance of: scholarly article
title: Products of involutions in \(O^ +(V)\)
zbMATH Open document ID: 0623.20036
DOI: 10.1016/0024-3795(87)90092-9
author: Frieder Knüppel
author: Klaus Nielsen
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let V be a finite-dimensional vector space over a commutative field K whose characteristic is distinct from 2. Assume V is endowed with a nondegenerate symmetric bilinear form. Let \(O^+(V)=\{\pi \in O(V):\) det \(\pi\) \(=1\}\). The authors show: An element \(\pi \in O^+(V)\) is a product of two involutions if and only if dim \(V\not\equiv 2 mod 4\) or an orthogonal decomposition of V into orthogonally indecomposable \(\pi\)- modules contains a \(\pi\)-module of odd dimension.
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 51F25
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 4010779
zbMATH Keywords: product of involutions
zbMATH Keywords: special orthogonal group
zbMATH Keywords: symmetric bilinear form
zbMATH Keywords: orthogonal decomposition
zbMATH Keywords: orthogonally indecomposable \(\pi \)- modules
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90092-9
OpenAlex ID: W2003625272
cites work: Product of two involutions
cites work: Q5632776
cites work: On bireflectionality and trireflectionality of orthogonal groups
cites work: Q5553361
description: scientific article; zbMATH DE number 4010779