Endomorphism Algebras of Maximal Rigid Objects in Cluster Tubes
نویسنده
چکیده
Given a maximal rigid object T of the cluster tube, we 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 turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the 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 the endomorphism algebras of maximal rigid objects. 2000 Mathematics Subject Classifications: 18E30, 16G10, 16E35.
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