Abstract:This paper is the first part of a series that intends to study resolving subcategories for gentle algebras over an algebraically closed field $\mathbb{K}$.
In a general setting, we improve the precision of Takahashi's algorithm for resolving closure calculations in well-behaved abelian categories. Then, we modify the geometric model of Baur--Coelho-Simões and Opper--Plamondon--Schroll to compute such subcategories for gentle quivers that have a finite global dimension.
Finally, we focus on gentle quivers $(Q,R)$ such that $Q$ is a directed tree, and we study monogeneous resolving subcategories, which are the ones generated by a single non-projective indecomposable $\mathbb{K}Q/\langle R \rangle$-module. Moreover, we prove that these subcategories are the join-irreducible elements of the poset of all resolving subcategories ordered by inclusion.
From: Benjalmin Dequêne [view email]
[v1]
Fri, 28 Feb 2025 12:29:23 UTC (52 KB)
[v2]
Fri, 3 Oct 2025 09:52:56 UTC (53 KB)
[v3]
Wed, 9 Sep 2026 17:55:16 UTC (56 KB)
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