Cancellative Elliptic Artin Monoids

TL;DR

This paper introduces new presentations for elliptic Artin groups, proves the cancellativity of the associated monoids, and lays groundwork for Garside structures, addressing previous issues in the literature.

Contribution

It provides novel presentations for elliptic Artin monoids and establishes their cancellativity, enabling further structural analysis.

Findings

Elliptic monoids are cancellative with new presentations

Addresses previous non-cancellativity issues in elliptic Artin monoids

Lays foundation for Garside structures in elliptic Artin groups

Abstract

We define new presentations for elliptic Artin groups. We also show that the elliptic monoids defined by these presentations are cancellative. This solves the failure of cancellativity for the presentations of elliptic Artin monoids that were introduced before in the literature. Our approach also paves the way to construct Garside structures for elliptic Artin monoids and groups.