杨-巴克斯特方程的代数-几何方法及相关主题

Publications De L'institut Mathematique Pub Date : 2012-07-11 DOI:10.2298/PIM1205025D

V. Dragović

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引用次数: 3

摘要

我们回顾了Yang-Baxter方程4 × 4解的代数-几何方法的结果。我们进一步强调了与双反射定理、庞塞勒波性和欧拉-查尔斯对应有关的一些几何性质。我们在数学物理中提出了一个分类列表，具有类似的几何背景，与圆锥铅笔有关。在结论部分，我们通过对初等n值群的计算实验，引入了判别可因式多项式的概念。

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

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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Publications De L'institut Mathematique

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