Mutation invariant functions on cluster ensembles
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Mutation invariant functions on cluster ensembles. / Kaufman, Dani.
I: Journal of Pure and Applied Algebra, Bind 228, Nr. 2, 107495, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Mutation invariant functions on cluster ensembles
AU - Kaufman, Dani
N1 - Publisher Copyright: © 2023 The Author(s)
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Cluster algebras
KW - Cluster ensembles
KW - Markov numbers
KW - Somos sequences
KW - Teichmuller spaces
UR - http://www.scopus.com/inward/record.url?scp=85166538318&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2023.107495
DO - 10.1016/j.jpaa.2023.107495
M3 - Journal article
AN - SCOPUS:85166538318
VL - 228
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 2
M1 - 107495
ER -
ID: 362935438