Endomorphisms of Artin groups of type $\tilde A_n$

TL;DR

This paper classifies the endomorphisms of the Artin group of affine type A_n for n, providing a comprehensive understanding of their structure.

Contribution

It offers the first complete classification of endomorphisms for Artin groups of affine type A_n when n.

Findings

Classified all endomorphisms of A_n Artin groups for n

Identified structural properties unique to affine type A_n groups

Enhanced understanding of automorphism groups of affine Artin groups

Abstract

We determine a classification of the endomorphisms of the Artin group of affine type $\tilde A_n$ for $n\ge 4$.