Abstract
The aim of this paper is to consider the relation between $$\mathsf {Lie}$$-isoclinism and isomorphism of two pairs of Leibniz algebras. We show that, unlike the absolute case for finite dimensional Lie algebras, these concepts are not identical, even if the pairs of Leibniz algebras are $$\mathsf {Lie}$$-stem. Moreover, throughout the paper, we provide some conditions under which $$\mathsf {Lie}$$-isoclinism and isomorphism of $$\mathsf {Lie}$$-stem Leibniz algebras are equal. In order to get this equality, the concept of factor set is studied as well.
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