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2-CY-tilted algebras that are not Jacobian

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arxiv 1403.6814 v1 pith:FSCURAEZ submitted 2014-03-26 math.RT

Sefi Ladkani This is my paper · ORCID
classification math.RT
keywords algebrascy-tiltedcategoriescertaincharacteristicconstructfractionallyjacobian
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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 $G_2$.

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Cited by 1 Pith paper

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  1. On syzygy categories over Iwanaga-Gorenstein algebras: Reduction, minimality and finiteness

    math.RT 2025-10 conditional novelty 7.0 of 10

    Syzygy categories over 2-Calabi-Yau tilted algebras are generated by the radicals of the projective modules, and idempotent reduction is governed by an explicit functor giving six equivalent conditions for the syzygy ...

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