Vol. 15, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Friezes satisfying higher $\mathrm{SL}_k$-determinants

Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko and Gordana Todorov

Appendix: Michael Cuntz and Pierre-Guy Plamondon

Vol. 15 (2021), No. 1, 29–68
Abstract

In this article, we construct SLk-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 SLk-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 SLk-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 E6.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.236.212.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
frieze pattern, mesh frieze, unitary frieze, cluster category, Grassmannian, Iyama–Yoshino reduction
Mathematical Subject Classification 2010
Primary: 05E10
Secondary: 13F60, 14M15, 16G20, 18D99
Milestones
Received: 15 January 2019
Revised: 23 April 2020
Accepted: 27 June 2020
Published: 1 March 2021
Authors
Karin Baur
School of Mathematics
University of Leeds
Leeds
United Kingdom
Eleonore Faber
School of Mathematics
University of Leeds
Leeds
United Kingdom
Sira Gratz
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom
Khrystyna Serhiyenko
Department of Mathematics
University of Kentucky
Lexington, KY
United States
Gordana Todorov
Department of Mathematics
Northeastern University
Boston, MA
United States
Michael Cuntz
Leibniz Universität Hannover
Institut für Algebra, Zahlentheorie und diskrete Mathematik
Fakultät für Mathematik und Physik
Hannover
Germany
Pierre-Guy Plamondon
Laboratoire de Mathématiques de Versailles
UVSQ, CNRS, Université Paris-Saclay
Versailles
France