An introduction to higher cluster categories

Abstract

In this survey, we give an overview over some aspects of the set of tilting objects in an m-cluster category, with focus on those properties which are valid for all m ≥ 1. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation. © 2011 Iranian Mathematical Society.