Hone, Andrew N.W. (2021) Deformations of cluster mutations and invariant presymplectic forms. Letters in Mathematical Physics, . ISSN 03779017. (Submitted) (KAR id:89747)
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Abstract
We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4 we find suitable conditions such that the deformation produces a twoparameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higherdimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to fourdimensional symplectic maps arising as reductions of the discrete sineGordon equation.
Item Type:  Article 

Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QC Physics > QC20 Mathematical Physics 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Andrew Hone 
Date Deposited:  12 Aug 2021 16:25 UTC 
Last Modified:  23 Aug 2021 11:11 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/89747 (The current URI for this page, for reference purposes) 
Hone, Andrew N.W.:  https://orcid.org/0000000197807369 
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