Publication details

Friezes satisfying higher slk-determinants

authored by
Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko, Gordana Todorov, Michael Cuntz, Pierre Guy Plamondon
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.

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
External Organisation(s)
University of Leeds
University of Glasgow
University of Kentucky
Northeastern University
Université Paris-Saclay
Type
Article
Journal
Algebra and Number Theory
Volume
15
Pages
29-68
No. of pages
40
ISSN
1937-0652
Publication date
01.03.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Algebra and Number Theory
Electronic version(s)
https://doi.org/10.2140/ant.2021.15.29 (Access: Closed)