Hom-Bol algebras

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) Homalgebra 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. Relying on the well-known classification of real two-dimensional Bol algebras, examples of real twodimensional Hom-Bol algebras are given.