Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 033, 9 pages      arXiv:0911.2895
Contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems”

On Quadrirational Yang-Baxter Maps

V.G. Papageorgiou a, Yu.B. Suris b, A.G. Tongas c and A.P. Veselov d, e
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) School of Mathematics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
e) Moscow State University, Moscow 119899, Russia

Received November 15, 2009, in final form March 26, 2010; Published online April 16, 2010

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.

Key words: Yang-Baxter maps; birational maps; integrability.

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