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Distributive laws between the Three Graces
Theory and applications of categories, Tome 34 (2019), pp. 1317-1342 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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By the Three Graces we refer, following J.-L. Loday, to the algebraic operads Ass, Com, and Lie, each generated by a single binary operation; algebras over these operads are respectively associative, commutative associative, and Lie. We classify all distributive laws (in the categorical sense of Beck) between these three operads. Some of our results depend on the computer algebra system Maple, especially its packages LinearAlgebra and Groebner.

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Classification : Primary 18D50. Secondary 13P10, 16R10, 16S10, 16S37, 16W10, 17B60, 17B63, 18-04, 68W30.
Keywords: Algebraic operads, distributive laws, Koszul duality, associative algebras, commutative associative algebras, Lie algebras, Poisson algebras, linear algebra over polynomial rings, Gr\"obner bases for polynomial ideals, computer algebra 
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     author = {Murray Bremner and Martin Markl},
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Murray Bremner; Martin Markl. Distributive laws between the Three Graces. Theory and applications of categories, Tome 34 (2019), pp. 1317-1342. http://geodesic.mathdoc.fr/item/TAC_2019_34_a40/