English

Distributive laws between the Three Graces

Algebraic Topology 2019-01-09 v2 Category Theory Rings and Algebras

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.

Keywords

Cite

@article{arxiv.1809.08191,
  title  = {Distributive laws between the Three Graces},
  author = {Murray Bremner and Martin Markl},
  journal= {arXiv preprint arXiv:1809.08191},
  year   = {2019}
}

Comments

19 pages. The analysis of magmatic-associative laws improved

R2 v1 2026-06-23T04:14:14.597Z