Special identities for Bol algebras

Date
2012-04-01
Authors
Hentzel, Irvin
Peresi, Luiz
Hentzel, Irvin
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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.

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<p>This article is published as Hentzel, Irvin R., and Luiz A. Peresi. "Special identities for Bol algebras." Linear Algebra and its Applications 436, no. 7 (2012): 2315-2330. doi: <a href="https://doi.org/10.1016/j.laa.2011.09.021" target="_blank" title="Persistent link using digital object identifier">10.1016/j.laa.2011.09.021</a>. Posted with permission.</p>
Keywords
Bol algebras, Polynomial identities, Computational methods, Representations of the symmetric group
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