Indecomposable Modules in the Grassmannian Cluster Category \rm CM(B_5,10)

2021/07/20 by Dusko Bogdanic, Ivan-Vanja Boroja
Mathematics · #math.RT #math.RA #msc:05E10 #msc:16G50

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published as Kragujevac Journal of Mathematics Volume 48(6) (2024), Pages 907-920 · arXiv admin note: text overlap with arXiv:2107.03503. text overlap with arXiv:2011.14176

arxiv created 2021/07/20 · arxiv updated 2021/11/02

Abstract

In this paper we study indecomposable rank 2 modules in the Grassmannian cluster category \rm CM(B_5,10). This is the smallest wild case containing modules whose profile layers are 5-interlacing. We construct all rank 2 indecomposable modules with filtration \i,i+2,i+4,i+6,i+8\| \i+1,i+3,i+5,i+7,i+9\, classify them up to isomorphism, and parameterize all infinite families of non-isomorphic rank 2 modules.

Citations

• Decomposable extensions between rank 1 modules in Grassmannian cluster categories
• Construction of Rank 2 Indecomposable Modules in Grassmannian Cluster Categories