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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 033, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.033 (Mi sigma490) 		 
This article is cited in 27 scientific papers (total in 28 papers)

On Quadrirational Yang–Baxter Maps

V. G. Papageorgioua, Yu. B. Surisb, A. G. Tongasc, A. P. Veselovde

a Department of Mathematics, University of Patras, 26 500 Patras, Greece
b Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
c Department of Applied Mathematics, University of Crete, 714 09 Heraklion, Greece
d Moscow State University, Moscow 119899, Russia
e School of Mathematics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
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DOI: https://doi.org/10.3842/SIGMA.2010.033
Abstract: 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.
Keywords: Yang–Baxter maps; birational maps; integrability.
Received: November 15, 2009; in final form March 26, 2010; Published online April 16, 2010
Bibliographic databases:
Document Type: Article
MSC: 14E07; 14H70; 37K20
Language: English
Citation: V. G. Papageorgiou, Yu. B. Suris, A. G. Tongas, A. P. Veselov, “On Quadrirational Yang–Baxter Maps”, SIGMA, 6 (2010), 033, 9 pp.
Citation in format AMSBIB
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\paper On Quadrirational Yang--Baxter Maps
\jour SIGMA
\yr 2010
\vol 6
\papernumber 033
\totalpages 9
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    • This publication is cited in the following 28 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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