Tubular Jacobian Algebras

Abstract

We show that the endomorphism ring of each cluster tilting object in a tubular cluster category is a finite dimensional Jacobian algebra which is tame of polynomial growth. Moreover, these Jacobian algebras are given by a quiver with a non-degenerate potential and mutation of cluster tilting objects is compatible with mutation of QPs.

21 pages, v3: exposition improved after referee report, include now more details about iterated tubular algebras and about the compatibility between mutation of cluster tilting objects and mutation of QPs. Exposition about iterated tubular coverings shortened. To appear in Algebras and Representation Theory

References in corpus (3)

• On triangulated orbit categories
• The representation type of Jacobian algebras
• Deformed Calabi-Yau Completions

Cited by in corpus (8)

• The representation type of Jacobian algebras
• Density of $g$-vector cones from triangulated surfaces
• ${\tau }^2$-stable tilting complexes over weighted projective lines
• Cluster categories from Grassmannians and root combinatorics
• Tame algebras have dense $\mathbf{g}$-vector fans
• Acyclic cluster algebras with dense $g$-vector fans
• Compatibility degree of cluster complexes
• Denominator vectors and dimension vectors from triangulated surfaces