Baur, K orcid.org/0000-0002-7665-476X, Bogdanic, D and Elsener, AG (2020) Cluster Categories from Grassmannians and Root Combinatorics. Nagoya Mathematical Journal, 240. pp. 322-354. ISSN 0027-7630
Abstract
The category of Cohen–Macaulay modules of an algebra 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 -planes in -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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been published in a revised form in Nagoya Mathematical Journal https://doi.org/10.1017/nmj.2019.14. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2019 Foundation Nagoya Mathematical Journal. |
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: | 21 Jun 2019 09:19 |
Last Modified: | 16 Dec 2020 09:30 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/nmj.2019.14 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147525 |