Coloured quiver mutation for higher cluster categories

TL;DR

This paper introduces a mutation operation on coloured quivers linked to higher cluster categories, providing a combinatorial method and algorithm for understanding tilting objects and their Gabriel quivers.

Contribution

It defines a new mutation operation on coloured quivers for higher cluster categories and demonstrates its compatibility with tilting object mutations.

Findings

Mutation operation on coloured quivers is compatible with tilting object mutation

Provides an algorithm to determine Gabriel quivers of tilting objects

Establishes a combinatorial approach to tilting in higher cluster categories

Abstract

We define mutation on coloured quivers associated to tilting objects in higher cluster categories. We show that this operation is compatible with the mutation operation on the tilting objects. This gives a combinatorial approach to tilting in higher cluster categories and especially an algorithm to determine the Gabriel quivers of tilting objects in such categories.