string modules
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2019 ◽  
Vol 72 (6) ◽  
pp. 1551-1580 ◽  
Author(s):  
Thomas Brüstle ◽  
Guillaume Douville ◽  
Kaveh Mousavand ◽  
Hugh Thomas ◽  
Emine Yıldırım

AbstractFor $A$ 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.


2019 ◽  
Vol 47 (12) ◽  
pp. 4969-4988
Author(s):  
Yohny Calderón-Henao ◽  
Hernán Giraldo ◽  
Ricardo Rueda-Robayo ◽  
José A. Vélez-Marulanda

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