Abstract:This paper is the third part of a series that intends to study the resolving subcategories for gentle algebras over an algebraically closed field $\mathbb{K}$.
As in the previous two papers, we continue to focus on gentle trees $(Q,R)$. Via a modified surface model for gentle algebras with finite global dimension, we developed combinatorial, poset, and quiver representation techniques that allow one to calculate all the resolving subcategories of $\mathbb{K}Q/\langle R \rangle$-mod. Furthermore, they enable one to calculate the resolving subcategory generated by any collection of $\mathbb{K}Q/\langle R \rangle$-modules.
In this paper, based on those techniques, we give a combinatorial realization of the Auslander--Reiten one-to-one correspondence between resolving subcategories and tilting modules in $\mathbb{K}Q/\langle R \rangle$-mod.
From: Benjalmin Dequêne [view email]
[v1]
Fri, 19 Jun 2026 13:41:24 UTC (37 KB)
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