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arXiv · 2403.07810

A geometric model for the module category of a string algebra

Karin Baur·Raquel Coelho Simoes
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Abstract

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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Karin Baur, Raquel Coelho Simoes. 2024-03-12. A geometric model for the module category of a string algebra. https://arxiv.org/abs/2403.07810

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