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IMI/Publicaţii/QRS/Ediţii/QRS v.21, n.2 (30), 2013/

Hom-Bol algebras

Authors: S. Attan and A. Nourou Issa

Abstract

Hom-Bol algebras are defined as a twisted generalization of (left) Bol algebras. Hom-Bol algebras generalize multiplicative Hom-Lie triple systems in the same way as Bol algebras generalize Lie triple systems. The notion of an nth derived (binary) Hom-algebra is extended to the one of an nth derived binary-ternary Hom-algebra and it is shown that the category of Hom-Bol algebras is closed under the process of taking nth derived Hom-algebras. It is also closed by self-morphisms of binary-ternary Hom-algebras. Every Bol algebra is twisted into a Hom-Bol algebra. Some examples of low-dimensional Hom-Bol algebras are given.

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