论文标题
有限类型的群集代数的晶格结构和非简单的Ingalls-thomas Boovestion
Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection
论文作者
论文摘要
在本文中，我们证明了有限类型集群代数中一组簇的晶格结构对某些Geiss-Leclerc-Schröer（GLS）路径代数的扭转晶格和$ C $ -C $ -CAMBRIAN LATTICE。我们通过明确描述有限类型的集群代数的交换震颤来证明这一点。具体而言，我们证明，这些颤动是由支持$τ$的模块在GLS路径代数中以及由$ c $ c $ cluss形成的模块形成的质量形状的，该模块是由$ c $ - c $ clusters组成的。
In this paper, we demonstrate that the lattice structure of a set of clusters in a cluster algebra of finite type is anti-isomorphic to the torsion lattice of a certain Geiss-Leclerc-Schröer (GLS) path algebra and to the $c$-Cambrian lattice. We prove this by explicitly describing the exchange quivers of cluster algebras of finite type. Specifically, we prove that these quivers are anti-isomorphic to those formed by support $τ$-tilting modules in GLS path algebras and to those formed by $c$-clusters consisting of almost positive roots.
