A geometric model for the module category of a skew-gentle algebra

Bin Zhu; Ping He; Yu Zhou

A geometric model for the module category of a skew-gentle algebra

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arxiv 2004.11136 v4 pith:L52XK2V3 submitted 2020-04-23 math.RT math.RA

Ping He , Yu Zhou , Bin Zhu This is my paper · ORCID

classification math.RTmath.RA

keywords taggedalgebrascurvesmodulespermissibleskew-gentleadmissiblealgebra

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abstract

In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain indecomposable modules, interpret the Auslander-Reiten translation via the tagged rotation, and show intersection-dimension formulas. As an application, we classify support $\tau$-tilting modules via maximal collections of non-crossing tagged generalized permissible curves.

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A geometric model for the non-$\tau$-rigid modules of type $\widetilde{D}_n$
math.RT 2025-07 conditional novelty 6.0 of 10

Colored admissible tagged edges in a twice-punctured disk model the non-tau-rigid modules of type \widetilde{D}_n and satisfy an intersection-dimension formula.

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