Geodesic
On the Combinatorics of Gentle Algebras
Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1551-1580

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DOI

For $A$ a gentle algebra, and $X$ and $Y$ string modules, we construct a combinatorial basis for $\operatorname{Hom}(X,\unicode[STIX]{x1D70F}Y)$. We use this to describe support $\unicode[STIX]{x1D70F}$-tilting modules for $A$. We give a combinatorial realization of maps in both directions realizing the bijection between support $\unicode[STIX]{x1D70F}$-tilting modules and functorially finite torsion classes. We give an explicit basis of $\operatorname{Ext}^{1}(Y,X)$ 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.
DOI : 10.4153/S0008414X19000397
Mots-clés : gentle algebras, τ-tilting theory 
Brüstle, Thomas; Douville, Guillaume; Mousavand, Kaveh; Thomas, Hugh; Yıldırım, Emine. On the Combinatorics of Gentle Algebras. Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1551-1580. doi: 10.4153/S0008414X19000397
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     title = {On the {Combinatorics} of {Gentle} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {1551--1580},
     year = {2020},
     volume = {72},
     number = {6},
     doi = {10.4153/S0008414X19000397},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000397/}
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