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arXiv · 1912.05519

Distributive laws between the operads Lie and Com

Murray Bremner·Vladimir Dotsenko
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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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Murray Bremner, Vladimir Dotsenko. 2019-12-11. Distributive laws between the operads Lie and Com. https://doi.org/10.1142/s021819672050054x

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