Representations and derivations of Hom-Lie conformal superalgebras

Abstract

In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some applications to the study of deformations of regular Hom-Lie conformal superalgebras. Finally, we introduce derivations of multiplicative Hom-Lie conformal superalgebras and study their properties.

Cohomology and conformal derivations of BiHom-Lie conformal superalgebras

“…In [15], the authors developed cohomology theory of Hom-Lie conformal algebras, discussed some applications to the study of deformations of regular Hom-Lie conformal algebras and introduced derivations of multiplicative Hom-Lie conformal algebras. Motivated by these results, authors, in [8], introduced the notion of representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, they developed their cohomology group and discuss some applications to the study of deformation theory.…”