Authors: Dragović, Vladimir 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Algebro-geometric approach to the Yang-Baxter equation and related topics
Journal: Publications de l'Institut Mathematique
Volume: 91
Issue: 1
First page: 25
Last page: 48
Issue Date: 11-Jul-2012
Rank: M23
ISSN: 0350-1302
DOI: 10.2298/PIM1205025D
We review the results of algebro-geometric approach to 4 × 4 solutions of the Yang-Baxter equation. We emphasis some further geometric properties, connected with the double-reflection theorem, the Poncelet porism and the Euler-Chasles correspondence. We present a list of classifications in Mathematical Physics with a similar geometric background, related to pencils of conics. In the conclusion, we introduce a notion of discriminantly factorizable polynomials as a result of a computational experiment with elementary n-valued groups.
Publisher: Mathematical Institute of the SASA
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Mathematical Physics Group of the University of Lisbon, Project Probabilistic approach to finite and infinite dimensional dynamical systems, PTDC/MAT/104173/2008

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