CLUSTER CATEGORIES FROM GRASSMANNIANS AND ROOT COMBINATORICS
CLUSTER CATEGORIES FROM GRASSMANNIANS AND ROOT COMBINATORICS
复制标题
DOI：
10.1017/nmj.2019.14
复制
发表时间：
2020-12-01
影响因子：
0.8
通讯作者：
Elsener, Ana Garcia
中科院分区：
文献类型：
--
作者：
Baur, Karin;Bogdanic, Dusko;Elsener, Ana Garcia
Jensen等人使用了代数BK；n的Cohen-Macaulay模范畴。(Grassman簇代数的一个范畴，Proc.朗德。数学课。SoC。(3)113(2)(2016)，185{212)给出了n维空间中k平面的Grassman齐次坐标环上的簇代数结构的加性分类。在本文中，我们找到了规范的Auslander-Reiten序列，并研究了这一范畴的Auslander-Reiten平移周期。此外，我们还给出了任意秩Cohen-Macaulay模的一个显式构造。然后，我们利用我们的结果建立了相关Kac-Moody代数在TAME情形下的2阶刚性不可分解模与2次实根之间的对应关系。
The category of Cohen-Macaulay modules of an algebra Bk;n is used in Jensen et al. (A categorification of Grassmannian cluster algebras, Proc. Lond. Math. Soc. (3) 113(2) (2016), 185{212) to give an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. In this paper, we find canonical Auslander-Reiten sequences and study the Auslander-Reiten translation periodicity for this category. Furthermore, we give an explicit construction of Cohen-Macaulay modules of arbitrary rank. We then use our results to establish a correspondence between rigid indecomposable modules of rank 2 and real roots of degree 2 for the associated Kac-Moody algebra in the tame cases.