From frieze patterns to cluster categories

Abstract

Motivated by Conway and Coxeter's combinatorial results concerning frieze patterns, we sketch an introduction to the theory of cluster algebras and cluster categories for acyclic quivers. The goal is to show how these more abstract theories provide a conceptual explanation for phenomena concerning friezes, principally integrality and periodicity.

31 pages. Notes for lecture series at LMS Autumn Algebra School, October 2020; final version, published in LMS Lecture Notes (Modern Trends in Algebra and Representation Theory)

References in corpus (7)

• On triangulated orbit categories
• Transport of structure in higher homological algebra
• Cluster algebras IV: Coefficients
• Monoidal categorification of cluster algebras II
• Calabi-Yau properties of Postnikov diagrams
• Frieze patterns with coefficients
• Cluster algebras III: Upper bounds and double Bruhat cells

Cited by in corpus (1)

• When frieze patterns meet Y-systems: Y-frieze patterns