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 |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| 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| _version_ | 1862640058363805696 |
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| author | Morier-Genoud, S. |
| author_facet | Morier-Genoud, S. |
| citation_txt | Symplectic Frieze Patterns / S. Morier-Genoud // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T21:25:04Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210299 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:04Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Symplectic Frieze Patterns Morier-Genoud, S. |
| title | Symplectic Frieze Patterns |
| title_full | Symplectic Frieze Patterns |
| title_fullStr | Symplectic Frieze Patterns |
| title_full_unstemmed | Symplectic Frieze Patterns |
| title_short | Symplectic Frieze Patterns |
| title_sort | symplectic frieze patterns |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210299 |
| work_keys_str_mv | AT moriergenouds symplecticfriezepatterns |