Algebro-geometric approach to the Yang-Baxter equation and related topics | Zendy

Vladimir Dragović | Zendy

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Algebro-geometric approach to the Yang-Baxter equation and related topics

Author(s) -

Vladimir Dragović

Publication year - 2012

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1205025d

Subject(s) - conic section , euler's formula , mathematics , reflection (computer programming) , algebra over a field , pure mathematics , computer science , mathematical analysis , geometry , programming language

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.

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