Graded identities for tensor products of matrix (super)algebras over the Grassmann algebra

dc.creatorDi Vincenzo, OM
dc.creatorKoshlukov, P
dc.creatorSantulo, EA
dc.date2010
dc.date42005
dc.date2014-11-19T23:32:58Z
dc.date2015-11-26T17:09:26Z
dc.date2014-11-19T23:32:58Z
dc.date2015-11-26T17:09:26Z
dc.date.accessioned2018-03-28T23:58:04Z
dc.date.available2018-03-28T23:58:04Z
dc.identifierLinear Algebra And Its Applications. Elsevier Science Inc, v. 432, n. 41700, n. 780, n. 795, 2010.
dc.identifier0024-3795
dc.identifierWOS:000272929800025
dc.identifier10.1016/j.laa.2009.09.021
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/68148
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/68148
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/68148
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1280623
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionIn this paper we study the graded identities satisfied by the superalgebras M(a,b) over the Grassmann algebra and by their tensor products. These algebras play a crucial role in the theory developed by A. Kemer that led to the solution of the long standing Specht problem. It is well known that over a field of characteristic 0, the algebras M(pr)+q(s,ps)+q(r) and M(p.q) circle times M(r,s) satisfy the same ordinary polynomial identities. By means of describing the corresponding graded identities we prove that the T-ideal of the former algebra is contained in the T-ideal of the latter. Furthermore the inclusion is proper at least in case (r, s) = (1, 1). Finally we deal with the graded identities satisfied by algebras of type M(2n-1),2(n-1) and relate these graded identities to the ones of tensor powers of the Grassmann algebra. Our proofs are combinatorial and rely on the relationship between graded and ordinary identities as well as on appropriate models for the corresponding relatively free graded algebras. (C) 2009 Elsevier Inc. All rights reserved.
dc.description432
dc.description41700
dc.description780
dc.description795
dc.descriptionMIUR
dc.descriptionUniversita della Basilicata
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionCNPq [302651/2008-0]
dc.descriptionFAPESP [2005/60337-2, 03107793-4]
dc.languageen
dc.publisherElsevier Science Inc
dc.publisherNew York
dc.publisherEUA
dc.relationLinear Algebra And Its Applications
dc.relationLinear Alg. Appl.
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectGraded identities
dc.subjectPI equivalence
dc.subjectMatrices over Grassmann algebras
dc.subjectRelatively free algebras
dc.subjectPolynomial-identities
dc.subjectPrime Algebras
dc.subjectOrder-n
dc.titleGraded identities for tensor products of matrix (super)algebras over the Grassmann algebra
dc.typeArtículos de revistas


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