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A geometric model for the module category of a string algebra

2024/03/12 by Karin Baur, Baur, Karin, Raquel Coelho Simões +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2403.07810

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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