On Quadrirational Yang-Baxter Maps
We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter map...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146351 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Quadrirational Yang-Baxter Maps / V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas, A.P. Veselov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862579586982739968 |
|---|---|
| author | Papageorgiou, V.G. Suris, Yu.B. Tongas, A.G. Veselov, A.P. |
| author_facet | Papageorgiou, V.G. Suris, Yu.B. Tongas, A.G. Veselov, A.P. |
| citation_txt | On Quadrirational Yang-Baxter Maps / V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas, A.P. Veselov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.
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| first_indexed | 2025-11-26T19:15:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146351 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T19:15:26Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Papageorgiou, V.G. Suris, Yu.B. Tongas, A.G. Veselov, A.P. 2019-02-09T09:22:36Z 2019-02-09T09:22:36Z 2010 On Quadrirational Yang-Baxter Maps / V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas, A.P. Veselov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14E07; 14H70; 37K20 DOI:10.3842/SIGMA.2010.033 https://nasplib.isofts.kiev.ua/handle/123456789/146351 We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics. This paper is a contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and UltraDiscrete Integrable Systems” (March 30 – April 3, 2009, University of Glasgow, UK). The full collection is available at http://www.emis.de/journals/SIGMA/GADUDIS2009.html.
 This work had been started in May 2007, when one of the authors (APV) visited Patras within the Erasmus-Socrates exchange programme, and completed at the Isaac Newton Institute for Mathematical Sciences in Cambridge during the programme on Discrete Integrable Systems in the spring semester 2009. The work of APV was also partially supported by the European RTN ENIGMA (contract MRTN-CT-2004-5652) and EPSRC (grant EP/E004008/1). We are grateful to V. Adler for useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Quadrirational Yang-Baxter Maps Article published earlier |
| spellingShingle | On Quadrirational Yang-Baxter Maps Papageorgiou, V.G. Suris, Yu.B. Tongas, A.G. Veselov, A.P. |
| title | On Quadrirational Yang-Baxter Maps |
| title_full | On Quadrirational Yang-Baxter Maps |
| title_fullStr | On Quadrirational Yang-Baxter Maps |
| title_full_unstemmed | On Quadrirational Yang-Baxter Maps |
| title_short | On Quadrirational Yang-Baxter Maps |
| title_sort | on quadrirational yang-baxter maps |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146351 |
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