论文标题
较高的Auslander代数的较高宽子类别的分类
Classification of higher wide subcategories for higher Auslander algebras of type A
论文作者
论文摘要
Abelian类别的子类别$ \ MATHSCR {W} $，如果在内核，凝胶和扩展下关闭，则称其为宽。广泛的子类别在表示理论中引起了人们的兴趣，因为它们与其他同源物体和组合对象的联系，以及由Ingalls-Thomas和Marks-šťovíček建立的。 如果$ d \ geqslant 1 $是整数，则Jasso介绍了$ d $ - 阿贝尔类别的概念，其中内核，凝胶和扩展名被更长的复合体取代。可以将广泛的子类别推广到这种情况。 $ d $ - 阿贝尔类别的重要示例作为$ d $ -cluster倾斜子类别$ \ Mathscr {m} _ {n，n，d} $ of $ \ operatatorName {mod} a_n^{d-1 {d-1} $本文对$ \ mathscr {m} _ {n，d} $的宽子类别进行了组合描述，以我们所谓的非交流集合。
A subcategory $\mathscr{W}$ of an abelian category is called wide if it is closed under kernels, cokernels, and extensions. Wide subcategories are of interest in representation theory because of their links to other homological and combinatorial objects, established among others by Ingalls-Thomas and Marks-Šťovíček. If $d \geqslant 1$ is an integer, then Jasso introduced the notion of $d$-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes. Wide subcategories can be generalised to this situation. Important examples of $d$-abelian categories arise as the $d$-cluster tilting subcategories $\mathscr{M}_{n,d}$ of $\operatorname{mod} A_n^{d-1}$, where $A_n^{d-1}$ is a higher Auslander algebra of type $A$ in the sense of Iyama. This paper gives a combinatorial description of the wide subcategories of $\mathscr{M}_{n,d}$ in terms of what we call non-interlacing collections.
