Artículos de revistas
Polynomial identities for the ternary cyclic sum
Date
2009Registration in:
LINEAR & MULTILINEAR ALGEBRA, v.57, n.6, p.595-608, 2009
0308-1087
10.1080/03081080802267748
Author
BREMNER, Murray R.
PERESI, Luiz A.
Institutions
Abstract
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.