2-CY-tilted algebras that are not Jacobian

Abstract

Over any field of positive characteristic we construct 2-CY-tilted algebras that are not Jacobian algebras of quivers with potentials. As a remedy, we propose an extension of the notion of a potential, called hyperpotential, that allows to prove that certain algebras defined over fields of positive characteristic are 2-CY-tilted even if they do not arise from potentials. In another direction, we compute the fractionally Calabi-Yau dimensions of certain orbit categories of fractionally CY triangulated categories. As an application, we construct a cluster category of type $G_2$.

arXiv comment18 pages

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Cited by in corpus (4)

• Algebras of quasi-quaternion type
• From groups to clusters
• Gentle $m$-Calabi-Yau tilted algebras
• Periodicity of cluster tilting objects