Polynomial identities for the ternary cyclic sum
| Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
|---|---|
| Data(s) |
20/10/2012
20/10/2012
2009
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| Resumo |
We 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. NSERC NSERC University of Saskatchewan University of Saskatchewan University of Sao Paulo (USP) University of Sao Paulo (USP) |
| Identificador |
LINEAR & MULTILINEAR ALGEBRA, v.57, n.6, p.595-608, 2009 0308-1087 http://producao.usp.br/handle/BDPI/30610 10.1080/03081080802267748 |
| Idioma(s) |
eng |
| Publicador |
TAYLOR & FRANCIS LTD |
| Relação |
Linear & Multilinear Algebra |
| Direitos |
restrictedAccess Copyright TAYLOR & FRANCIS LTD |
| Palavras-Chave | #non-associative algebra #polynomial identities #trilinear operations #lattice basis reduction #representation theory of the symmetric group #computational linear algebra #Mathematics |
| Tipo |
article original article publishedVersion |
