Artículos de revistas
Special identities for Bol algebras
Date
2012Registration in:
LINEAR ALGEBRA AND ITS APPLICATIONS, NEW YORK, v. 436, n. 7, supl. 1, Part 3, pp. 2315-2330, APR 1, 2012
0024-3795
10.1016/j.laa.2011.09.021
Author
Hentzel, Irvin R.
Peresi, Luiz A.
Institutions
Abstract
Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.