Homological splitting results for modules over Leibniz algebras

TL;DR

This paper presents a unified splitting theorem for Ext groups in modules over Leibniz algebras, generalizing previous results by Loday and Pirashvili, applicable to symmetric and antisymmetric modules.

Contribution

It introduces a generalized splitting result for Ext in Leibniz algebra modules, expanding the scope of earlier work to include symmetric and antisymmetric modules.

Findings

Unified splitting result for Ext in Leibniz modules

Generalization of Loday and Pirashvili's results

Applicable to symmetric and antisymmetric modules

Abstract

A unified splitting result for Ext calculated in the category of modules over a Leibniz algebra is given for the case where coefficients are either both symmetric modules or both antisymmetric modules. This is a generalization of results of Loday and Pirashvili and others.