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

Harvard

Kaufman, D 2024, 'Mutation invariant functions on cluster ensembles', Journal of Pure and Applied Algebra, bind 228, nr. 2, 107495. https://doi.org/10.1016/j.jpaa.2023.107495

APA

Kaufman, D. (2024). Mutation invariant functions on cluster ensembles. Journal of Pure and Applied Algebra, 228(2), [107495]. https://doi.org/10.1016/j.jpaa.2023.107495

Vancouver

Kaufman D. Mutation invariant functions on cluster ensembles. Journal of Pure and Applied Algebra. 2024;228(2). 107495. https://doi.org/10.1016/j.jpaa.2023.107495

Author

Kaufman, Dani. / Mutation invariant functions on cluster ensembles. I: Journal of Pure and Applied Algebra. 2024 ; Bind 228, Nr. 2.

Bibtex

@article{eeb8b87da2ee4c7d9cd67079da908010,
title = "Mutation invariant functions on cluster ensembles",
abstract = "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 Teichm{\"u}ller theory of surfaces.",
keywords = "Cluster algebras, Cluster ensembles, Markov numbers, Somos sequences, Teichmuller spaces",
author = "Dani Kaufman",
note = "Publisher Copyright: {\textcopyright} 2023 The Author(s)",
year = "2024",
doi = "10.1016/j.jpaa.2023.107495",
language = "English",
volume = "228",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier BV * North-Holland",
number = "2",

}

RIS

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