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LINEAR RELATIONS AND INTEGRABILITY FOR CLUSTER ALGEBRAS FROM AFFINE QUIVERS
Published online by Cambridge University Press: 13 August 2020
Abstract
We consider frieze sequences corresponding to sequences of cluster mutations for affine D- and E-type quivers. We show that the cluster variables satisfy linear recurrences with periodic coefficients, which imply the constant coefficient relations found by Keller and Scherotzke. Viewing the frieze sequence as a discrete dynamical system, we reduce it to a symplectic map on a lower dimensional space and prove Liouville integrability of the latter.
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- Research Article
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- © The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
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