Multicomponent pentagon maps

TL;DR

This paper characterizes multicomponent pentagon maps through associative-like conditions on n-ary magmas, introduces parametric variants, and presents a method to generate families of such maps.

Contribution

It provides necessary and sufficient conditions for multicomponent pentagon maps and a procedure to generate related families from a given map.

Findings

Characterization of multicomponent pentagon maps

Introduction of parametric pentagon maps

Procedure to generate families of pentagon maps

Abstract

We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps. We obtain parametric-pentagon maps and we propose a procedure that generates families of multicomponent pentagon and entwining pentagon maps from a given pentagon map.