A relation between tilting graphs and cluster-tilting graphs of hereditary algebras

Abstract

We give the condition of isomorphisms between tilting graphs and cluster-tilting graphs of hereditary algebras. As a conclusion, it is proved that a graph is a skeleton graph of Stasheff polytope if and only if it is both the tilting graph of a hereditary algebra and also the cluster-tilting graph of another hereditary algebra. At last, when comparing such uniformity, the geometric realizations of simplicial complexes associated with tilting modules and clustertilting objects are discussed respectively.

Keywords

Tilting graph / cluster-tilting graph / cluster category / Stasheff polytope / linear quiver

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