A New Approach to Defining Cochain Complexes for dual Leibniz algebra

TL;DR

This paper introduces a novel method to embed dual Leibniz algebra cohomology into Lie algebra cohomology, simplifying computations and revealing new structural insights.

Contribution

It constructs a cochain map that embeds dual Leibniz cohomology into Lie algebra cohomology, bridging the two theories.

Findings

Reduces dual Leibniz cohomology to classical Lie algebra cohomology

Provides computational simplifications

Offers new structural insights into dual Leibniz algebras

Abstract

We construct a cochain map embedding the cohomology complex of any dual Leibniz algebra $B$ into the Lie algebra cochain complex of $\mathfrak{g} \otimes B$, where $\mathfrak{g}$ is a Leibniz algebra. This reduces the study of dual Leibniz cohomology to classical Lie algebra cohomology, yielding computational simplifications and new structural insights.