Friezes satisfying higher slk-determinants

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)29-68
Number of pages40
JournalAlgebra and Number Theory
Issue number1
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Mathematical Sciences Publishers.


  • Cluster category
  • Frieze pattern
  • Grassmannian
  • Iyama–Yoshino reduction
  • Mesh frieze
  • Unitary frieze

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Friezes satisfying higher slk-determinants'. Together they form a unique fingerprint.

Cite this