Integrable Systems and Cluster Algebras

Michael Gekhtman; Anton Izosimov

doi:10.1016/B978-0-323-95703-8.00029-X

Integrable Systems and Cluster Algebras

Michael Gekhtman
, Anton Izosimov

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

We review several constructions of integrable systems with an underlying cluster algebra structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on perfect networks and the Goncharov-Kenyon approach based on the dimer model. We also discuss results of Galashin and Pylyavskyy on integrability of T-systems.

Original language	English (US)
Title of host publication	Encyclopedia of Mathematical Physics, Second Edition
Subtitle of host publication	Volumes 1-5
Publisher	Elsevier
Pages	V3:294-V3:308
Volume	1-5
ISBN (Electronic)	9780323957069
ISBN (Print)	9780323957038
DOIs	https://doi.org/10.1016/B978-0-323-95703-8.00029-X
State	Published - Jan 1 2024
Externally published	Yes

Keywords

Cluster algebras
Directed networks
Integrable
Systems
T-systems

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/B978-0-323-95703-8.00029-X

Cite this

@inbook{52cd3c4de0034318b10ec29d8a3dbcf6,

title = "Integrable Systems and Cluster Algebras",

abstract = "We review several constructions of integrable systems with an underlying cluster algebra structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on perfect networks and the Goncharov-Kenyon approach based on the dimer model. We also discuss results of Galashin and Pylyavskyy on integrability of T-systems.",

keywords = "Cluster algebras, Directed networks, Integrable, Systems, T-systems",

author = "Michael Gekhtman and Anton Izosimov",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd. All rights are reserved.",

year = "2024",

month = jan,

day = "1",

doi = "10.1016/B978-0-323-95703-8.00029-X",

language = "English (US)",

isbn = "9780323957038",

volume = "1-5",

pages = "V3:294--V3:308",

booktitle = "Encyclopedia of Mathematical Physics, Second Edition",

publisher = "Elsevier",

}

TY - CHAP

T1 - Integrable Systems and Cluster Algebras

AU - Gekhtman, Michael

AU - Izosimov, Anton

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We review several constructions of integrable systems with an underlying cluster algebra structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on perfect networks and the Goncharov-Kenyon approach based on the dimer model. We also discuss results of Galashin and Pylyavskyy on integrability of T-systems.

AB - We review several constructions of integrable systems with an underlying cluster algebra structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on perfect networks and the Goncharov-Kenyon approach based on the dimer model. We also discuss results of Galashin and Pylyavskyy on integrability of T-systems.

KW - Cluster algebras

KW - Directed networks

KW - Integrable

KW - Systems

KW - T-systems

UR - https://www.scopus.com/pages/publications/85211158775

UR - https://www.scopus.com/pages/publications/85211158775#tab=citedBy

U2 - 10.1016/B978-0-323-95703-8.00029-X

DO - 10.1016/B978-0-323-95703-8.00029-X

M3 - Chapter

AN - SCOPUS:85211158775

SN - 9780323957038

VL - 1-5

SP - V3:294-V3:308

BT - Encyclopedia of Mathematical Physics, Second Edition

PB - Elsevier

ER -

Integrable Systems and Cluster Algebras

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this