Baur, K orcid.org/0000-0002-7665-476X, Bogdanic, D and Li, J-R (2023) Construction of rank 2 indecomposable modules in Grassmannian cluster categories. Advanced Studies in Pure Mathematics, 88. pp. 1-45. ISSN 0920-1971
Abstract
The category CM(Bk,n) of Cohen-Macaulay modules over a quotient Bk,n of a preprojective algebra provides a categorification of the cluster algebra structure on the coordinate ring of the Grassmannian variety of k-dimensional subspaces in Cn, [13]. Among the indecomposable modules in this category are the rank 1 modules which are in bijection with k-subsets of {1,2,…,n}, and their explicit construction has been given by Jensen, King and Su. These are the building blocks of the category as any module in CM(Bk,n) can be filtered by them. In this paper we give an explicit construction of rank 2 modules. With this, we give all indecomposable rank 2 modules in the cases when k=3 and k=4. In particular, we cover the tame cases and go beyond them. We also characterise the modules among them which are uniquely determined by their filtrations. For k≥4, we exhibit infinite families of non-isomorphic rank 2 modules having the same filtration.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article published in Advanced Studies in Pure Mathematics, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Cohen-Macaulay modules , Grassmannian cluster categories , rank 2 modules |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Jun 2023 13:29 |
Last Modified: | 06 Jun 2023 13:37 |
Status: | Published |
Publisher: | Mathematical Society of Japan |
Identification Number: | 10.2969/aspm/08810001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:199232 |