Friezes satisfying higher SL_k-determinants

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2021) Friezes satisfying higher SL_k-determinants. Algebra and Number Theory, 15(1), pp. 29-68. (doi: 10.2140/ant.2021.15.29)

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In this article, we construct SL k -friezes using Plücker coordinates, making use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of k -spaces in n -space via the Plücker embedding. When this cluster algebra is of finite type, the SL k -friezes are in bijection with the so-called mesh friezes of the corresponding Grassmannian cluster category. These are collections of positive integers on the AR-quiver of the category with relations inherited from the mesh relations on the category. In these finite type cases, many of the SL k -friezes arise from specializing a cluster to 1. These are called unitary. We use Iyama–Yoshino reduction to analyze the nonunitary 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 E 6 .

Item Type:Articles
Additional Information:Baur was supported by FWF grants P 30549-N26 and W1230. She is supported by a Royal Society Wolfson Research Merit Award. Faber is a Marie Skłodowska-Curie fellow at the University of Leeds (funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 789580). Serhiyenko was supported by NSF Postdoctoral Fellowship MSPRF — 1502881.
Glasgow Author(s) Enlighten ID:Gratz, Dr Sira
Authors: Baur, K., Faber, E., Gratz, S., Serhiyenko, K., and Todorov, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebra and Number Theory
Publisher:Mathematical Sciences Publishers
ISSN (Online):1944-7833
Published Online:01 March 2021
Copyright Holders:Copyright © 2021 Mathematical Sciences Publishers
First Published:First published in Algebra and Number Theory 15(1):29-68
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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