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Cluster categories from Grassmannians and root combinatorics. (arXiv:1807.05181v1 [math.RT])

来源于:arXiv
The category of Cohen-Macaulay modules of an algebra $B_{k,n}$ is used in [JKS16] to give an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$-planes in $n$-space. We study the Auslander-Reiten translation periodicity for this category, extensions, and we find canonical Auslander-Reiten sequences. Then, we focus on the tame cases and establish a correspondence between certain rigid indecomposable modules of rank 2 and real roots of degree 2 for the associated Kac-Moody algebra. We also an give explicit construction of indecomposable rank 2 modules. 查看全文>>