Polynomial identities for the ternary cyclic sum

dc.creatorBREMNER, Murray R.
dc.creatorPERESI, Luiz A.
dc.date.accessioned2012-10-20T04:50:23Z
dc.date.accessioned2018-07-04T15:46:45Z
dc.date.available2012-10-20T04:50:23Z
dc.date.available2018-07-04T15:46:45Z
dc.date.created2012-10-20T04:50:23Z
dc.date.issued2009
dc.identifierLINEAR & MULTILINEAR ALGEBRA, v.57, n.6, p.595-608, 2009
dc.identifier0308-1087
dc.identifierhttp://producao.usp.br/handle/BDPI/30610
dc.identifier10.1080/03081080802267748
dc.identifierhttp://dx.doi.org/10.1080/03081080802267748
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1627249
dc.description.abstractWe simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.
dc.languageeng
dc.publisherTAYLOR & FRANCIS LTD
dc.relationLinear & Multilinear Algebra
dc.rightsCopyright TAYLOR & FRANCIS LTD
dc.rightsrestrictedAccess
dc.subjectnon-associative algebra
dc.subjectpolynomial identities
dc.subjecttrilinear operations
dc.subjectlattice basis reduction
dc.subjectrepresentation theory of the symmetric group
dc.subjectcomputational linear algebra
dc.titlePolynomial identities for the ternary cyclic sum
dc.typeArtículos de revistas


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