# Equivariant one-parameter formal deformations of Hom-Leibniz algebras

## TL;DR

This paper introduces a new cohomology theory for multiplicative Hom-Leibniz algebras that governs their deformations, extending the framework to include equivariant cases with finite group actions.

## Contribution

It develops a novel cohomology and deformation theory for Hom-Leibniz algebras, including an extension to equivariant settings with group actions.

## Key findings

- Defined a new cohomology controlling deformations.
- Extended deformation theory to equivariant Hom-Leibniz algebras.
- Established foundational results for equivariant deformation analysis.

## Abstract

Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as developed here are also extended to equvariant context, under the presence of finite group actions on Hom-Leibniz algebras.