August, J, Cheung, M-W, Faber, E orcid.org/0000-0003-2541-8916 et al. (2 more authors) (2023) Cluster structures for the A∞ singularity. Journal of the London Mathematical Society, 107 (6). pp. 2121-2149. ISSN 0024-6107
Abstract
We study a category C2$\mathcal {C}_2$ of Z$\mathbb {Z}$-graded maximal Cohen-Macaulay (MCM) modules over the A∞$A_\infty$ curve singularity and demonstrate that it has infinite type A$A$ cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type A$A$ cluster categories of Holm–Jørgensen, Fisher and Paquette–Yıldırım. As a consequence, C2$\mathcal {C}_2$ has cluster tilting subcategories modelled by certain triangulations of the (completed) ∞$\infty$-gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategories, and show that these subcategories and their mutations exhibit the combinatorics of the completed ∞$\infty$-gon.
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Copyright, Publisher and Additional Information: | © 2023 The Authors. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. | ||||||
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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) | ||||||
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Depositing User: | Symplectic Publications | ||||||
Date Deposited: | 31 Mar 2023 09:34 | ||||||
Last Modified: | 23 Nov 2023 16:32 | ||||||
Status: | Published | ||||||
Publisher: | Wiley | ||||||
Identification Number: | https://doi.org/10.1112/jlms.12735 |