Orbifold diagrams
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Publication:6352285
DOI10.1016/J.JALGEBRA.2022.10.039arXiv2010.13812MaRDI QIDQ6352285
Karin Baur, Andrea Pasquali, Diego Velasco
Publication date: 26 October 2020
Abstract: 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.
Combinatorial aspects of representation theory (05E10) Cohen-Macaulay modules in associative algebras (16G50) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)
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