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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>>