Periodic Coxeter matrices
type: Item
instance of: scholarly article
title: Periodic Coxeter matrices
zbMATH Open document ID: 1019.15015
DOI: 10.1016/S0024-3795(02)00405-6
published in: Linear Algebra and its Applications
publication date: 2003-05-25T00:00:00Z
review text: Cartan \((C_A)\) and Coxeter \((\varphi_A)\) matrices are considered. Conditions are given on the eigenvalues of \(\varphi_A\), which imply the periodicity of \(\varphi_A\). If \(\varphi_A\) is periodic then the Euler form \(q_A(x)= xC_A^{-t}x^t\) is nonnegative. Examples are given. The relation of the Coxeter matrices \(\varphi_A\) and \(\varphi_B\) for a one-point extension \(A=B[M]\) of a \(k\)-algebra \(B\) by a \(B\)-module \(M\) is studied.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 1915484
zbMATH Keywords: Cartan matrix
zbMATH Keywords: Coxeter matrix
zbMATH Keywords: Euler quadratic form
zbMATH Keywords: periodic matrix
zbMATH Keywords: eigenvalues
author: José A. de la Peña
MaRDI profile type: Publication
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full work available at URL: s0024-3795(02)00405-6
OpenAlex ID: W1969455280
description: scientific article; zbMATH DE number 1915484