Friezes satisfying higher sl_k-determinants

verfasst von

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

Abstract

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 E₆.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

University of Leeds
University of Glasgow
University of Kentucky
Northeastern University
Universität Paris-Saclay

Typ

Artikel

Journal

Algebra and Number Theory

Band

15

Seiten

29-68

Anzahl der Seiten

40

ISSN

1937-0652

Publikationsdatum

01.03.2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.2140/ant.2021.15.29 (Zugang: Geschlossen)