Article, 2024

Mutation invariant functions on cluster ensembles

In: Journal of Pure and Applied Algebra, ISSN 0022-4049, Volume 228, 2, 10.1016/j.jpaa.2023.107495

Contributors (1)

Kaufman D. (0000-0002-1519-6718) [1]


  1. [1] University of Copenhagen
  2. [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD]


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.


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