A Geometric Model for the Module Category of a Gentle Algebra-Reference-Cited by-同舟云学术

A Geometric Model for the Module Category of a Gentle Algebra

Published:2019-07-31 Issue:15 Volume:2021 Page:11357-11392
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Baur Karin¹²,Coelho Simões Raquel³

Affiliation:

1. Karl-Franzens-Universitat Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria

2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

3. Centro de Análise Funcional, Estruturas Lineares e Aplicações, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, Piso 2, 1749-016 Lisboa, Portugal

Abstract

Abstract In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian algebras of triangulations of surfaces and the notion of surface algebras. We use this description to give a geometric model of the module category of any gentle algebra.

Funder

Fundação para a Ciência e Tecnologia

FWF Der Wissenschaftsfonds

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/15/11357/39458089/rnz150.pdf

Reference42 articles.

1. Cluster categories for algebras of global dimension 2 and quivers with potential;Amiot;Ann. Inst. Fourier (Grenoble),2009

2. Gentle algebras arising from surface triangulations;Assem;Algebra Number Theory,2010