ENDOMORPHISM ALGEBRAS OF MAXIMAL RIGID OBJECTS IN CLUSTER TUBES.

Given u maximal rigid object T of the cluster tube, ice determine the objects finitely presented by T. We then use the method of Keller and Reiten to show that the endomorphism algebra of T is Gorenstein and of finite representation type, as first shown by Vatne. This algebra tarns out to he the Jacohian algebra of a certain quiver with potential, when the characteristic of the base field is not .?. We study how this quiver with potential changes when T is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects. [ABSTRACT FROM AUTHOR]