Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras

The celebrated Diamond Lemma of Bergman gives an effectively verifiable criterion of uniqueness of normal forms for term rewriting in associative algebras. We revisit that result in the context of deformation theory and homotopical algebra; this leads to a new proof using multiplicative free resolutions. Specifically, our main result states that every such resolution of an algebra with monomial relations gives rise to its own Diamond Lemma, where Bergman’s condition of “resolvable ambiguities” is precisely the first nontrivial component of the Maurer–Cartan equation in the corresponding tangent complex. The same approach works for many other algebraic structures, emphasizing the relevance of computing resolutions of algebras with monomial relations.

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Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras

Cited by 2 publications

References 35 publications

Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases

Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases

Tangent complexes and the Diamond Lemma

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