Products of quasireflections and transvections over local rings
type: Item
instance of: scholarly article
title: Products of quasireflections and transvections over local rings
zbMATH Open document ID: 0639.20031
DOI: 10.1007/BF01222386
author: Rolfdieter Frank
author: Erich W. Ellers
published in: Journal of Geometry
publication date: 1988-01-01T00:00:00Z
review text: Let R be a commutative local ring, and M a free R-module of rank n, endowed with a metric structure given by a sesquilinear form or a quadratic form. The authors show that every isometry \(\pi\) of M is a product of quasi reflections and transvections. They determine the minimal number of factors in any factorization of \(\pi\) if the path of \(\pi\) is a subspace, and an upper bound on the number for all other isometries.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 51F25
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 11E08
zbMATH DE Number: 4042159
zbMATH Keywords: unitary groups
zbMATH Keywords: orthogonal groups
zbMATH Keywords: factorization of isometries into reflections, quasireflections, and transvections
zbMATH Keywords: symplectic groups
zbMATH Keywords: local ring
zbMATH Keywords: sesquilinear form
zbMATH Keywords: quadratic form
zbMATH Keywords: product of quasi reflections and transvections
zbMATH Keywords: minimal number of factors
zbMATH Keywords: upper bound
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042159