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Orbifold diagrams

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arxiv 2010.13812 v2 pith:2CX3STJU submitted 2020-10-26 math.RT math.CO

Karin Baur , Andrea Pasquali , Diego Velasco This is my paper · ORCID
classification math.RTmath.CO
keywords diagramsalgebraorbifolddiskpostnikovdiagramjacobianalternating
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We study alternating strand diagrams on the disk with an orbifold point. These are quotients by rotation of Postnikov diagrams on the disk, and we call them orbifold diagrams. We associate a quiver with potential to each orbifold diagram, in such a way that its Jacobian algebra and the one associated to the covering Postnikov diagram are related by a skew-group algebra construction. We moreover realise this Jacobian algebra as the endomorphism algebra of a certain explicit cluster-tilting object. This is similar to (and relies on) a result by Baur-King-Marsh for Postnikov diagrams on the disk.

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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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