Cluster-Tilted Algebra Of G₂ Type

Fomin-Zelevinsky defined and studied cluster algebras in 2002.The cluster-tilting theory introduced for categorifying cluster algebras is one of the hot topics of represen-tation theory of finite dimensional algebras in the past ten years.Cluster-tilted algebras are the endomorphism algebras of cluster-tilting objects in cluster categories.This thesis studies cluster-tilted algebras of type G₂.It shows that the rank vectors of the inde-composableτ-rigid objects coincide the positive c-vectors of the cluster algebra of type G₂.