Some results on the second relative homology of Leibniz algebras

TL;DR

This paper investigates the second relative homology of Leibniz algebras, focusing on their structure and properties using non-abelian tensor products, especially for finite-dimensional nilpotent cases.

Contribution

It provides new insights into the second relative homology and stem covers of Leibniz algebras via non-abelian tensor products, extending previous algebraic understanding.

Findings

Determined the structure of second relative homology for direct sums of Leibniz algebras.

Characterized pairs of finite-dimensional nilpotent Leibniz algebras with specific properties.

Connected homological properties with algebraic structures using tensor products.

Abstract

In this paper, the structure of the second relative homology and the relative stem cover of the direct sum of two pairs of Leibniz algebras are determined by means of the non-abelian tensor product of Leibniz algebras. We also characterize all pairs of finite dimensional nilpotent Leibniz algebras such that...