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Type: Artigo de periódico
Title: Involutions for upper triangular matrix algebras
Author: Di Vincenzo, OM
Koshlukov, P
La Scala, R
Abstract: In this paper we describe completely the involutions of the first kind of the algebra UTn(F) of n x n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UTn(F) when n is even and a single class in the odd case. Furthermore we consider the algebra UT2(F) of the 2 x 2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincare) series and the codimension sequences of the respective relatively free algebras. Then we consider the *-polynomial identities for the algebra UT3(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UTn(F) of the n x n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities. (C) 2006 Elsevier Inc. All rights reserved.
Subject: involution
upper triangular matrices
identities with involution
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.aam.2005.07.004
Date Issue: 2006
Appears in Collections:Unicamp - Artigos e Outros Documentos

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