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