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math.RAAug 1, 2013
33
citations (OpenAlex)
authors
  • Greg Muller
institutions
  • Louisiana State University
arXiv abstractPDF
paper

A=U for Locally Acyclic Cluster Algebras

arXiv:1308.1141 · doi:10.3842/SIGMA.2014.094

Abstract

This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.

References in corpus (2)

  • Locally acyclic cluster algebras
  • Skein algebras and cluster algebras of marked surfaces

Cited by in corpus (13)

  • Domain wall formation and magnon localization in twisted chromium trihalides
  • Factoriality and class groups of cluster algebras
  • Singularities of locally acyclic cluster algebras
  • A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
  • Upper cluster algebras and choice of ground ring
  • Schemes of modules over gentle algebras and laminations of surfaces
  • Reddening Sequences for Banff Quivers and the Class P
  • The valuation pairing on an upper cluster algebra
  • Generic Caldero-Chapoton functions with coefficients and applications to surface cluster algebras
  • On the Generalized Cluster Algebras of Geometric Type
  • On class groups of upper cluster algebras
  • On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfaces
  • Machine Learning Mutation-Acyclicity of Quivers
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