Matthew Pressland
Published 2020-10-27Version 1
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.
Comments: 23 pages. Notes for lecture series at LMS Autumn Algebra School, October 2020
A bijection between $m$-cluster-tilting objects and $(m+2)$-angulations in $m$-cluster categories
$m$-cluster categories and $m$-replicated algebras
Notes on the cluster multiplication formulas for 2-Calabi-Yau categories
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