Distributive laws between the operads Lie and Com
Quantum Algebra
2020-10-15 v1 Category Theory
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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Cite
@article{arxiv.1912.05519,
title = {Distributive laws between the operads Lie and Com},
author = {Murray Bremner and Vladimir Dotsenko},
journal= {arXiv preprint arXiv:1912.05519},
year = {2020}
}
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8 pages