# On Leibniz superalgebras which even part is sl_2

## TL;DR

This paper classifies Leibniz superalgebras with an even part isomorphic to sl_2, focusing on cases where the odd part is an irreducible module, revealing existence only when the odd part has dimension two.

## Contribution

It provides a complete description of Leibniz superalgebras with even part sl_2 and irreducible odd modules, identifying the specific dimension where nontrivial structures occur.

## Key findings

- Existence of Leibniz superalgebras with odd part only when dim L_1=2
- Classification of such superalgebras with irreducible modules
- Explicit description of the algebraic structures involved

## Abstract

This article deals with a Leibniz superalgebras $L=L_0\oplus L_1,$ whose even part is a simple Lie algebra $\mathfrak{sl}_2$. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on $\mathfrak{sl}_2 $. We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of $dim L_1=2.$