Products of quasireflections and transvections over local rings
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.
factorization of isometries into reflections, quasireflections, and transvections
product of quasi reflections and transvections
scientific article; zbMATH DE number 4042159
scientific article