论文标题
$ n \ mathbb {z} $ - nakayama代数的集群倾斜子类别
$n\mathbb{Z}$-cluster tilting subcategories for Nakayama algebras
论文作者
论文摘要
$ n \ mathbb {z} $ - 集群倾斜子类别是更高维度的Auslander-Reiten理论的理想设置。我们给出了$ n \ mathbb {z} $的完整分类 - nakayama代数的模块类别的集群倾斜子类别。特别是，我们表明，有三种nakayama代数可以接纳$ n \ mathbb {z} $ - 集群倾斜子类别：有限的全球维度，自我指示性和非iwanaga-gorenstein。只有自我调查的人才能接受多个$ n \ mathbb {z} $ - 群集倾斜子类别。第二作者已经表明，每个这样的$ n \ mathbb {z} $ - 群集倾斜子类别诱导$ n \ mathbb {z} $ - 相应奇点类别的群集倾斜子类别。对于分类中的每个中山代数，我们描述了其奇异性类别，从其模块类别到其奇异性类别的规范函数，并提供了$ N \ Mathbb {Z} $ - 群集倾斜子类别的$ N \ Mathbb {Z} $的完整比较。这在很大程度上依赖于沉的结果，后者描述了所有Nakayama代数的奇异类别。
$n\mathbb{Z}$-cluster tilting subcategories are an ideal setting for higher dimensional Auslander-Reiten theory. We give a complete classification of $n\mathbb{Z}$-cluster tilting subcategories of module categories of Nakayama algebras. In particular, we show that there are three kinds of Nakayama algebras that admit $n\mathbb{Z}$-cluster tilting subcategories: finite global dimension, selfinjective and non-Iwanaga-Gorenstein. Only the selfinjective ones can admit more than one $n\mathbb{Z}$-cluster tilting subcategory. It has been shown by the second author, that each such $n\mathbb{Z}$-cluster tilting subcategory induces an $n\mathbb{Z}$-cluster tilting subcategory of the corresponding singularity category. For each Nakayama algebra in our classification, we describe its singularity category, the canonical functor from its module category to its singularity category, and provide a complete comparison of $n\mathbb{Z}$-cluster tilting subcategories in the module category and the singularity category. This relies heavily of results by Shen, who described the singularity categories of all Nakayama algebras.
