{"title":"ALGEBRO-GEOMETRIC APPROACH TO THE YANG-BAXTER EQUATION AND RELATED TOPICS","authors":"V. Dragović","doi":"10.2298/PIM1205025D","DOIUrl":null,"url":null,"abstract":"We review the results of algebro-geometric approach to 4 × 4 solutions of the \n Yang-Baxter equation. We emphasis some further geometric properties, \n connected with the double-reflection theorem, the Poncelet porism and the \n Euler-Chasles correspondence. We present a list of classifications in \n Mathematical Physics with a similar geometric background, related to pencils \n of conics. In the conclusion, we introduce a notion of discriminantly \n factorizable polynomials as a result of a computational experiment with \n elementary n-valued groups.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/PIM1205025D","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
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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