Some results on $\delta$-Hom-Jordan Lie conformal superalgebras

Abstract

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