Isoclinism and factor set in regular Hom-Lie Superalgebras

Abstract: Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in regular Hom-Lie superalgebras. Finally, we obtain that two finite same dimensional regular Hom-Lie superalgebras are isoclinic if and only if they are isomorphic.