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A geometric model for the module category of a skew-gentle algebra (2004.11136v4)
Published 23 Apr 2020 in math.RT and math.RA
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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