Hom- Bol algebras

Abstract

Hom-Bol algebras are defined as a twisted generalization of (left) bol algebra. 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.