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In this paper we introduce the concept of -Lie-isoclinism on non-Lie Leibniz algebras. Among the results obtained, we provide several characterizations of -Lie-isoclinic classes of Leibniz algebras. Also, we provide a characterization of -Lie-stem Leibniz algebras, and prove that every -Lie-isoclinic class of Leibniz algebras contains a -Lie-stem Leibniz algebra.

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