A geometric model for the module category of a skew-gentle algebra
P He, Y Zhou, B Zhu - Mathematische Zeitschrift, 2023 - Springer
P He, Y Zhou, B Zhu
Mathematische Zeitschrift, 2023•SpringerIn 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 τ-tilting modules via maximal
collections of non-crossing tagged generalized permissible curves.
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 τ-tilting modules via maximal
collections of non-crossing tagged generalized permissible curves.
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 -tilting modules via maximal collections of non-crossing tagged generalized permissible curves.
Springer
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