EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 91(105), pp. 25–48 (2012)

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ALGEBRO-GEOMETRIC APPROACH TO THE YANG–BAXTER EQUATION AND RELATED TOPICS

Vladimir Dragovic

Mathematical Institute SANU, Belgrade, Serbia

Abstract: We review the results of algebro-geometric approach to $4\times 4$ 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.

Classification (MSC2000): 14H70; 82B23; 37J35; 39A12

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Electronic fulltext finalized on: 10 May 2012. This page was last modified: 12 Jun 2012.

© 2012 Mathematical Institute of the Serbian Academy of Science and Arts
© 2012 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition