Abstract:In this paper, we introduce maximal green sequences of infinite length in abelian length categories and establish natural bijections among infinite maximal green sequences, finest stability data, and complete backward $\operatorname{Hom}$-orthogonal (briefly, CBHO) sequences of bricks.
For cluster quiver patterns (equivalently, cluster algebras) of infinite rank, we define maximal green sequences of infinite length via $c$-vectors. Moreover, we prove that under suitable conditions such a maximal green sequence in a cluster quiver pattern of infinite rank can be categorified as a maximal green sequence of torsion classes in the corresponding representation category via a specific construction, thereby providing an example of a maximal green sequence in an abelian length category. This framework establishes a connection between infinite maximal green sequences in representation theory and maximal green sequences for cluster algebras of infinite rank.
From: Fang Li [view email]
[v1]
Fri, 12 Jun 2026 15:30:20 UTC (34 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。