# Derivations and deformations of $\delta$-Jordan Lie supertriple systems

## TL;DR

This paper explores the algebraic structures of $\delta$-Jordan Lie supertriple systems, introducing derivations, representations, and cohomology, and investigates their deformations and Nijenhuis operators to understand their algebraic properties.

## Contribution

It introduces generalized derivations, representations, and studies cohomology and deformations of $\delta$-Jordan Lie supertriple systems, providing new insights into their structure.

## Key findings

- Defined generalized derivations and representations of $T$
- Analyzed low-dimensional cohomology and coboundary operators
- Studied deformations and Nijenhuis operators using cohomology

## Abstract

Let $T$ be a $\delta$-Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of $T$ and present some properties. Also, we study the low dimension cohomology and the coboundary operator of $T$, and then we investigate the deformations and Nijenhuis operators of $T$ by choosing some suitable cohomology.