论文标题
$ n $ - 集群倾斜子类别来自代表代数的胶合系统
$n$-cluster tilting subcategories from gluing systems of representation-directed algebras
论文作者
论文摘要
我们提出了一种构建$ n $ cluster-cluster倾斜子类别的新方法。我们的方法将Abelian类别的直接系统作为输入$ \ Mathcal {a} _i $具有某些子类别，并且在合理条件下，输出了可允许的目标$ \ Mathcal {a} $的直接系统的$ n $ cluster倾斜子类别。我们将此通用方法应用于模块类别的直接系统$ \ text {mod}λ_i$表示为代数的代数$λ_i$，并获得一个$ n $ -cluster倾斜子类别$ \ MATHCAL {M MATHCAL {M MATHCAL {m} $的模块类别$ \ text} $ \ Mathcal {C} $。在某些情况下，我们还构建了一个可允许的$ \ Mathbb {z} $ - $ \ Mathcal {C} $的操作。使用darpö-iyama的结果，我们获得了$ \ text {mod}的$ n $ clustruster倾斜子类别（\ mathcal {c}/\ mathbb {z}）$，其中$ \ mathcal {c}/\ mathbb {Z} $是相应的Orbit类别。我们表明，在这种情况下，$ \ text {mod}（\ mathcal {c}/\ mathbb {z}）$等同于有限维代数的模块类别。通过这种方式，我们构建了许多新的代表式代数的家庭，其模块类别承认$ n $ cluster倾斜模块。
We present a new way to construct $n$-cluster tilting subcategories of abelian categories. Our method takes as input a direct system of abelian categories $\mathcal{A}_i$ with certain subcategories and, under reasonable conditions, outputs an $n$-cluster tilting subcategory of an admissible target $\mathcal{A}$ of the direct system. We apply this general method to a direct system of module categories $\text{mod}Λ_i$ of representation-directed algebras $Λ_i$ and obtain an $n$-cluster tilting subcategory $\mathcal{M}$ of a module category $\text{mod}\mathcal{C}$ of a locally bounded Krull-Schmidt category $\mathcal{C}$. In certain cases we also construct an admissible $\mathbb{Z}$-action of $\mathcal{C}$. Using a result of Darpö-Iyama, we obtain an $n$-cluster tilting subcategory of $\text{mod}(\mathcal{C}/\mathbb{Z})$ where $\mathcal{C}/\mathbb{Z}$ is the corresponding orbit category. We show that in this case $\text{mod}(\mathcal{C}/\mathbb{Z})$ is equivalent to the module category of a finite-dimensional algebra. In this way we construct many new families of representation-finite algebras whose module categories admit $n$-cluster tilting modules.
