Deformed cluster maps of type A_2N

2024/02/28 by Grabowski, Jan E., Hone, Andrew N. W., Kim, Wookyung
#37J70 (Primary) 13F60 #39A36 #81R12 (Secondary) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2402.18310

Abstract

We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types A_2N, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for N≤ 3. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' operation on quivers which allows us to construct and study mutations in type A_2N from those in type A_2(N-1).

Related

• Integrable deformations of cluster maps of type D_2N
• Deformations of cluster mutations and invariant presymplectic forms
• New cluster algebras from old: integrability beyond Zamolodchikov periodicity
• Periodic Cluster Mutations and Related Integrable Maps
• Commuting integrable maps from a deformed D₄ cluster algebra