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A geometric model for the module category of a string algebra

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arxiv 2403.07810 v1 pith:QBB7UXQG submitted 2024-03-12 math.RT math.RA

Karin Baur , Raquel Coelho Simoes This is my paper · ORCID
classification math.RTmath.RA
keywords stringalgebraclassificationgeometricgivemodulealgebrasapplication
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In this paper, we give a geometric construction of string algebras and of their module categories. Our approach uses dissections of punctured Riemann surfaces with extra data at marked points, called labels. As an application, we give a classification of support tau-tilting modules in terms of arcs in such a tiled surface. In the case when the string algebra is gentle, we recover the classification given arXiv:2004.11136.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Affine Tamari Lattice

    math.CO 2025-02 conditional novelty 8.0 of 10

    New cyclic and affine Tamari lattices of sizes Catalan Bn and Dn are constructed and shown to govern maximal green sequence lengths for path algebras of oriented cycles.

  2. Homological rigidity of quiver representations over $\mathbb{F}_1$

    math.RT 2026-07 accept novelty 7.0 of 10

    Yoneda Ext groups of F1-quiver representations vanish in degrees >2 for every quiver, so global dimension is at most 2 and is classified by orientation type.

  3. A multiplication formula for cluster characters in gentle algebras

    math.RT 2025-02 conditional novelty 6.0 of 10

    A multiplication formula for cluster characters of gentle algebras is proved and used to interpret surface cluster exchange relations and type B/type A variable relations categorically.

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