Abstract
Let (g,n) be a pair of Leibniz algebras, where n is an ideal of g. In this article, we develop the concepts of the second relative homology and the relative stem cover of the pair (g,n). By constructing a version of the Hopf's formula for HL2(g,n), we prove the existence of relative stem covers for (g,n). We also give some inequalities and a certain upper bound for the dimension of HL2(g,n). In addition, we classify all pairs of finite dimensional nilpotent Leibniz algebras that have one or two steps distance to this upper bound.
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