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

## TL;DR

This paper develops the representation theory, cohomology, and derivations for $oldsymbol{ ext{} extit{ extdelta}- ext{Hom-Jordan Lie conformal superalgebras, providing new tools for their structural analysis and deformation study.

## Contribution

It introduces the representation and cohomology theories for $ extdelta$-Hom-Jordan Lie conformal superalgebras, expanding the understanding of their structure and deformations.

## Key findings

- Established the representation theory for $ extdelta$-Hom-Jordan Lie conformal superalgebras.
- Developed the cohomology theory and explored applications to deformations.
- Analyzed properties of derivations in this algebraic context.

## 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.