2-Graded polynomial identities for the Jordan algebra of the symmetric matrices of order two

dc.creatorKoshlukov, P
dc.creatorSilva, DDPS
dc.date2011
dc.dateFEB 1
dc.date2014-07-30T13:38:47Z
dc.date2015-11-26T17:28:50Z
dc.date2014-07-30T13:38:47Z
dc.date2015-11-26T17:28:50Z
dc.date.accessioned2018-03-29T00:15:55Z
dc.date.available2018-03-29T00:15:55Z
dc.identifierJournal Of Algebra. Academic Press Inc Elsevier Science, v. 327, n. 1, n. 236, n. 250, 2011.
dc.identifier0021-8693
dc.identifierWOS:000286285000012
dc.identifier10.1016/j.jalgebra.2010.09.045
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/52581
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/52581
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1285148
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionThe Jordan algebra of the symmetric matrices of order two over a field K has two natural gradings by Z(2), the cyclic group of order 2. We describe the graded polynomial identities for these two gradings when the base field is infinite and of characteristic different from 2. We exhibit bases for these identities in each of the two cases. In one of the cases we perform a series of computations in order to reduce the problem to dealing with associators while in the other case one employs methods and results from Invariant theory. Moreover we extend the latter grading to a Z(2)-grading on B(n), the Jordan algebra of a symmetric bilinear form in a vector space of dimension n (n = 1,2,..., infinity). We call this grading the scalar one since its even part consists only of the scalars. As a by-product we obtain finite bases of the Z(2)-graded identities for B(n). In fact the last result describes the weak Jordan polynomial identities for the pair (B(n), V(n)). (C) 2010 Elsevier Inc. All rights reserved.
dc.description327
dc.description1
dc.description236
dc.description250
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, 2010/50347-9, 2007/00447-4]
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.subjectGraded identities
dc.subjectJordan identities
dc.subjectFinite basis of identities
dc.subjectWeak identities
dc.subjectWeak Jordan identities
dc.subjectInvariant Theory
dc.subjectBilinear Form
dc.title2-Graded polynomial identities for the Jordan algebra of the symmetric matrices of order two
dc.typeArtículos de revistas


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