Cup-product for equivariant Leibniz cohomology and zinbiel algebras

TL;DR

This paper introduces a cup-product operation on equivariant Leibniz cohomology groups under finite group actions, establishing a graded zinbiel algebra structure that advances the understanding of algebraic symmetries.

Contribution

It defines equivariant cohomology for Leibniz algebras with finite group actions and proves the existence of a graded zinbiel algebra structure via a cup-product.

Findings

Existence of a cup-product making cohomology a zinbiel algebra

Construction of equivariant cohomology groups for Leibniz algebras

Extension of algebraic structures under group actions

Abstract

We study finite group actions on Leibniz algebras, define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology groups which makes it a graded zinbiel algebra.