On the combinatorics of gentle algebras
Canadian Journal of Mathematics, vol.72, no.6, pp.1551-1580, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 72 Issue: 6
- Publication Date: 2020
- Doi Number: 10.4153/s0008414x19000397
- Journal Name: Canadian Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Page Numbers: pp.1551-1580
- Keywords: Gentle algebras, τ-tilting theory
- Open Archive Collection: AVESIS Open Access Collection
- Galatasaray University Affiliated: Yes
Abstract
For A a gentle algebra, and X and Y string modules, we construct a combinatorial basis for Hom(X, τY). We use this to describe support τ-tilting modules for A. We give a combinatorial realization of maps in both directions realizing the bijection between support τ-tilting modules and functorially finite torsion classes. We give an explicit basis of Ext1(Y, X) as short exact sequences. We analyze several constructions given in a more restricted, combinatorial setting by McConville, showing that many but not all of them can be extended to general gentle algebras.