# Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras

## TL;DR

This paper investigates 3-dimensional Heisenberg Hom-Lie superalgebras by describing their structures, computing cohomology spaces, and analyzing their infinitesimal deformations to understand their algebraic properties.

## Contribution

It provides a detailed classification of Hom-Lie super structures and cohomology for 3D Heisenberg superalgebras, including deformation analysis, which is a novel contribution.

## Key findings

- Classification of Hom-Lie super structures
- Computation of cohomology spaces
- Characterization of infinitesimal deformations

## Abstract

In this paper, we study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras, we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal deformations.