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Distributive laws between the operads Lie and Com
Published 11 Dec 2019 in math.QA and math.CT | (1912.05519v1)
Abstract: Using methods of computer algebra, especially Gr\"obner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet-Loday formula deforming the Poisson operad into the associative operad.
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