Symplectic Frieze Patterns

We introduce a new class of friezes that is related to symplectic geometry. On the algebraic and combinatorics sides, this variant of friezes is related to the cluster algebras involving the Dynkin diagrams of type C₂ and Am. On the geometric side, they are related to the moduli space of Lagrangian...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Author: Morier-Genoud, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210299
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Symplectic Frieze Patterns / S. Morier-Genoud // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210299
record_format dspace
spelling Morier-Genoud, S.
2025-12-05T09:25:48Z
2019
Symplectic Frieze Patterns / S. Morier-Genoud // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 13F60; 05E10; 14N20; 53D30
arXiv: 1803.06001
https://nasplib.isofts.kiev.ua/handle/123456789/210299
https://doi.org/10.3842/SIGMA.2019.089
We introduce a new class of friezes that is related to symplectic geometry. On the algebraic and combinatorics sides, this variant of friezes is related to the cluster algebras involving the Dynkin diagrams of type C₂ and Am. On the geometric side, they are related to the moduli space of Lagrangian configurations of points in the 4-dimensional symplectic space introduced in [Conley C.H., Ovsienko V., Math. Ann. 375 (2019), 1105-1145]. Symplectic friezes share similar combinatorial properties to those of Coxeter friezes and SL-friezes.
I am deeply grateful to Valentin Ovsienko for sharing with me ideas and results of the preliminary version of [6]. I am also grateful to Michael Cuntz for computer calculations and Bernhard Keller for help with the applet [18]. I also want to thank Luc Pirio for stimulating discussions on the subject. This work is supported by the ANR project SC3A, ANR-15-CE40-0004-01.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Symplectic Frieze Patterns
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Symplectic Frieze Patterns
spellingShingle Symplectic Frieze Patterns
Morier-Genoud, S.
title_short Symplectic Frieze Patterns
title_full Symplectic Frieze Patterns
title_fullStr Symplectic Frieze Patterns
title_full_unstemmed Symplectic Frieze Patterns
title_sort symplectic frieze patterns
author Morier-Genoud, S.
author_facet Morier-Genoud, S.
publishDate 2019
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We introduce a new class of friezes that is related to symplectic geometry. On the algebraic and combinatorics sides, this variant of friezes is related to the cluster algebras involving the Dynkin diagrams of type C₂ and Am. On the geometric side, they are related to the moduli space of Lagrangian configurations of points in the 4-dimensional symplectic space introduced in [Conley C.H., Ovsienko V., Math. Ann. 375 (2019), 1105-1145]. Symplectic friezes share similar combinatorial properties to those of Coxeter friezes and SL-friezes.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210299
citation_txt Symplectic Frieze Patterns / S. Morier-Genoud // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.
work_keys_str_mv AT moriergenouds symplecticfriezepatterns
first_indexed 2025-12-07T21:25:04Z
last_indexed 2025-12-07T21:25:04Z
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