Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics
Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 25
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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 :
14H70 82B23 37J35 39A12
Vladimir Dragović. Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics. Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 25 . http://geodesic.mathdoc.fr/item/PIM_2012_N_S_91_105_a3/
@article{PIM_2012_N_S_91_105_a3,
author = {Vladimir Dragovi\'c},
title = {Algebro-geometric {Approach} to the {Yang-Baxter} {Equation} and {Related} {Topics}},
journal = {Publications de l'Institut Math\'ematique},
pages = {25 },
year = {2012},
volume = {_N_S_91},
number = {105},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2012_N_S_91_105_a3/}
}