August, J, Cheung, M-W, Faber, E orcid.org/0000-0003-2541-8916 et al. (2 more authors) (2023) Categories for Grassmannian Cluster Algebras of Infinite Rank. International Mathematics Research Notices. rnad004. ISSN 1073-7928
Abstract
We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian category of infinite rank is given as the category of graded maximal Cohen–Macaulay modules over a certain hypersurface singularity. We show that generically free modules of rank 1 in a Grassmannian category of infinite rank are in bijection with the Plücker coordinates in an appropriate Grassmannian cluster algebra of infinite rank. Moreover, this bijection is structure preserving, as it relates rigidity in the category to compatibility of Plücker coordinates. Along the way, we develop a combinatorial formula to compute the dimension of the Ext1
-spaces between any two generically free modules of rank 1 in the Grassmannian category of infinite rank.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. Published by Oxford University Press. All rights reserved. This is an author produced version of an article published in International Mathematics Research Notices. Uploaded in accordance with the publisher's self-archiving policy. |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/W007509/1 London Mathematical Society 11971 |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Feb 2023 15:21 |
Last Modified: | 27 Feb 2024 01:13 |
Status: | Published online |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnad004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195917 |