The centre of generic algebras of small PI algebras

dc.creatorKoshlukov, P
dc.creatorde Mello, TC
dc.date2013
dc.dateFEB 1
dc.date2014-08-01T18:23:17Z
dc.date2015-11-26T17:00:35Z
dc.date2014-08-01T18:23:17Z
dc.date2015-11-26T17:00:35Z
dc.date.accessioned2018-03-28T23:48:23Z
dc.date.available2018-03-28T23:48:23Z
dc.identifierJournal Of Algebra. Academic Press Inc Elsevier Science, v. 375, n. 109, n. 120, 2013.
dc.identifier0021-8693
dc.identifierWOS:000313466400009
dc.identifier10.1016/j.jalgebra.2012.11.018
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/78115
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/78115
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1278514
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionVerbally prime algebras are important in PI theory. They are well known over a field K of characteristic zero: 0 and K < T > (the trivial ones), M-n(K), M-n(E), M-ab(E). Here K < T > is the free associative algebra with free generators T, E is the infinite dimensional Grassmann algebra over K. M-n(K) and M-n(E) are the n x n matrices over K and over E, respectively. Moreover M-ab(E) are certain subalgebras of Ma+b(E), defined below. The generic algebras of these algebras have been studied extensively. Procesi gave a very tight description of the generic algebra of M-n(K). The situation is rather unclear for the remaining nontrivial verbally prime algebras. In this paper we study the centre of the generic algebra of M-11 (E) in two generators. We prove that this centre is a direct sum of the field and a nilpotent ideal (of the generic algebra). We describe the centre of this algebra. As a corollary we obtain that this centre contains nonscalar elements thus we answer a question posed by Berele. (C) 2012 Elsevier Inc. All rights reserved.
dc.description375
dc.description109
dc.description120
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 [304003/2011-5, 480139/2012-1]
dc.descriptionFAPESP [2010/50347-9]
dc.languageen
dc.publisherAcademic Press Inc Elsevier Science
dc.publisherSan Diego
dc.publisherEUA
dc.relationJournal Of Algebra
dc.relationJ. Algebra
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectGeneric algebras
dc.subjectCentral elements
dc.subjectPolynomial identities
dc.subjectMatrices over Grassmann algebras
dc.subjectPolynomial-identities
dc.subjectGrassmann Algebras
dc.subjectTrace Identities
dc.subjectInvariant-theory
dc.subjectMatrix Algebra
dc.subjectOrder-2
dc.titleThe centre of generic algebras of small PI algebras
dc.typeArtículos de revistas


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