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3 - From Frieze Patterns to Cluster Categories

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

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, such as integrality and periodicity.

Keywords

cluster algebrascluster categoriesacyclic quiversfrieze patterns
Type
Chapter
Information
Modern Trends in Algebra and Representation Theory , pp. 109 - 145
Publisher: Cambridge University Press
Print publication year: 2023

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