Mutation invariant functions on cluster ensembles

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We define the notion of a mutation invariant function on a cluster ensemble with respect to a group action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type of invariant ring and give many new examples. We show that these invariants have geometric and number theoretic interpretations, and classify them for ensembles associated to affine Dynkin diagrams. The primary tool used in this classification is the relationship between cluster algebras and the Teichmüller theory of surfaces.

Original languageEnglish
Article number107495
JournalJournal of Pure and Applied Algebra
Issue number2
Number of pages25
Publication statusPublished - 2024

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)

    Research areas

  • Cluster algebras, Cluster ensembles, Markov numbers, Somos sequences, Teichmuller spaces

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