Geometrization of Trigonometric Solutions of the Associative and Classical Yang–Baxter Equations
Geometrization of Trigonometric Solutions of the Associative and Classical Yang–Baxter Equations
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DOI：
10.1093/imrn/rnab304
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发表时间：
2020-06
影响因子：
1
通讯作者：
A. Polishchuk
中科院分区：
文献类型：
--
作者：
A. Polishchuk
我们描述了一个几何结构的所有非退化三角解的联想和经典的杨巴克斯特方程。在结合的情况下，解决方案来自算术亏格$1$的不可约节点曲线上的对称球面订单，而在李的情况下，他们来自同一曲线上的李代数的球面层。
We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang–Baxter equations. In the associative case, the solutions come from symmetric spherical orders over the irreducible nodal curve of arithmetic genus $1$, while in the Lie case they come from spherical sheaves of Lie algebras over the same curve.