March 12, 2024Open Access

A geometric model for the module category of a string algebra

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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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Baur et al. (Tue,) studied this question.

synapsesocial.com/papers/68e746d8b6db6435876bfc31 https://doi.org/https://doi.org/10.48550/arxiv.2403.07810

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