Abstract
In this paper, we elaborate Gröbner–Shirshov bases method for Leibniz (super)algebras. We show that there is a unique reduced Gröbner–Shirshov basis for every (graded) ideal of a free Leibniz (super)algebra. As applications, we construct linear bases of free metabelian Leibniz (super)algebras and new linear bases of free metabelian Lie algebras.
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