Minimal mutation-infinite quivers

TL;DR

This paper classifies minimal mutation-infinite quivers, including those from hyperbolic Coxeter simplices and exceptional cases, by using a series of moves to relate different classes.

Contribution

It provides a comprehensive classification of minimal mutation-infinite quivers, expanding beyond those derived from hyperbolic Coxeter simplices.

Findings

Classified minimal mutation-infinite quivers via moves

Linked classes to hyperbolic Coxeter simplices

Identified exceptional classes not related to simplices

Abstract

Quivers constructed from hyperbolic Coxeter simplices give examples of minimal mutation-infinite quivers, however they are not the only such quivers. We classify minimal mutation-infinite quivers through a number of moves and link the representatives of the classes with the hyperbolic Coxeter simplices, plus exceptional classes which are not related to simplices.