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Distributive laws between the Three Graces

2018/09/21 by Murray R. Bremner, Martin Markl, Bremner, Murray +1
Mathematics · #16R10 #16S10 #16S37 #16W10 #17B60 #17B63 #18-04 #18D5 (Primary) 13P10 #68W30 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1809.08191

openalex publication_date 2018/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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