Lattices of t-structures and thick subcategories for discrete cluster categories
Lattices of t-structures and thick subcategories for discrete cluster categories
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离散簇类别的 t 结构格和厚子类别
DOI：
10.1112/jlms.12705
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Gratz S
中科院分区：
文献类型：
--
作者：
Gratz S
我们对 Dynkin 类型 A$A$ 的任何离散簇类别 C(Z)$\mathcal {C}(\mathcal {Z})$ 中的 t 结构和厚子类别进行分类，并表明 C(Z)$\mathcal {C}(\mathcal {Z})$ 上的所有 t 结构的集合是包含过道的格子，其交集给出了交集。我们证明，以这种方式获得的 C(Z)$\mathcal {C}(\mathcal {Z})$ 上的 t 结构格和 C(Z)$\mathcal {C}(\mathcal {Z})$ 的厚子类别格都与 A$A$ 类型的非交叉分区格密切相关。特别是，此类类别上的非简并 t 结构的等价类格与有限线性有序集的非交叉分区格是同构的。
We classify t‐structures and thick subcategories in any discrete cluster category C(Z)$\mathcal {C}(\mathcal {Z})$ of Dynkin type A$A$, and show that the set of all t‐structures on C(Z)$\mathcal {C}(\mathcal {Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t‐structures on C(Z)$\mathcal {C}(\mathcal {Z})$ obtained in this way and the lattice of thick subcategories of C(Z)$\mathcal {C}(\mathcal {Z})$ are intimately related to the lattice of non‐crossing partitions of type A$A$. In particular, the lattice of equivalence classes of non‐degenerate t‐structures on such a category is isomorphic to the lattice of non‐crossing partitions of a finite linearly ordered set.