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Cluster Algebras and Discrete Integrability

Hone, Andrew N.W. and Lampe, P. and Kouloukas, Theodoros E. (2019) Cluster Algebras and Discrete Integrability. In: Euler, Norbert and Nucci, Maria Clara, eds. Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 2. CRC Press. ISBN 978-0-367-20847-9. E-ISBN 978-0-429-26374-3. (doi:10.1201/9780429263743) (KAR id:76592)

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https://doi.org/10.1201/9780429263743

Abstract

Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the context of cluster mutation. In particular, we give examples of birational maps that are integrable in the Liouville sense and arise from cluster algebras with periodicity, as well as examples of discrete Painleve equations that are derived from Y-systems.

Item Type: Book section
DOI/Identification number: 10.1201/9780429263743
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA901 Mechanics of deformable bodies, fluid mechanics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 18 Sep 2019 13:19 UTC
Last Modified: 06 May 2020 03:19 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/76592 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
Kouloukas, Theodoros E.: https://orcid.org/0000-0002-9903-6788
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