Deformations of compatible Hom-mock-Lie algebras

Abstract

In this paper, we study Hom-mock-Lie algebras as a twisted version of mock-Lie algebras. Also we consider a pair of Hom-mock-Lie algebras structures satisfying that any linear combination of the two Hom-mock-Lie structures is still a Hom-mock-Lie structure called compatible Hom-mock-Lie algebras and exhibit some related results. Next, we introduce the notion of representation of a compatible Hom-mock-Lie algebra. Finally, we study linear deformations of a compatible Hom-mock-Lie algebra.