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Given a maximal rigid object $T$ of the cluster tube, we determine theobjects finitely presented by $T$. We then use the method of Keller and Reitento show that the endomorphism algebra of $T$ is Gorenstein and of finiterepresentation type, as first shown by Vatne. This algebra turns out to be theJacobian algebra of a certain quiver with potential, when the characteristic ofthe base field is not 3. We study how this quiver with potential changes when$T$ is mutated. We also provide a derived equivalence classification for theendomorphism algebras of maximal rigid objects.

Endomorphism algebras of maximal rigid objects in cluster tubes