Baur, K orcid.org/0000-0002-7665-476X, Faber, E orcid.org/0000-0003-2541-8916, Gratz, S et al. (2 more authors) (2021) Friezes satisfying higher SLk-determinants. Algebra and Number Theory, 15 (1). pp. 29-68. ISSN 1937-0652
Abstract
In this article, we construct SLκ-friezes using Plücker coordinates, making
use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of κ-spaces in n-space via the Plücker embedding. When this cluster algebra is of finite type, the SLκ-friezes are in bijection with the so-called mesh friezes of the corresponding Grassmannian cluster category. These are collections of positive integers on the ARquiver of the category with relations inherited from the mesh relations on the category.
In these finite type cases, many of the SLκ-friezes arise from specialising a cluster to 1. These are called unitary. We use Iyama-Yoshino reduction to analyse the non-unitary friezes. With this, we provide an explanation for all known friezes of this kind. An appendix by Cuntz and Plamondon proves that there are 868 friezes of type Ε₆.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Mathematical Sciences Publishers. First published in Algebra and Number Theory in Vol. 15 (2021), No. 1, published by Mathematical Sciences Publishers. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | frieze pattern, mesh frieze, unitary frieze, cluster category, Grassmannian, Iyama–Yoshino reduction |
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: | 30 Jul 2020 15:45 |
Last Modified: | 23 Mar 2021 10:21 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers (MSP) |
Identification Number: | 10.2140/ant.2021.15.29 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:163712 |