On the second relative homology of Leibniz algebras

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 ( n)=n, ( g/ n)=m and (HL₂( g, n))=n(n+2m)-3.