Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations
Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations
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射影线循环和杨-巴克斯特方程三角解的梅西积
DOI：
10.1145/3173225.3173232
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
A. Polishchuk
中科院分区：
文献类型：
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作者：
A. Polishchuk
我们证明了结合Yang-Baxter方程（AYBE）对于$\Mat（N，\C）$（见数学AG/0008156）的一个非退化酉解$r（u，v）$在$u=0$的形式为$r（u，v）=\frac{1\ot 1}{u}+r_0（v）+.$满足量子Yang-Baxter方程，条件是$r_0（v）$到无迹矩阵的投影有周期.我们对AYBE的所有此类解进行了分类，扩展了Schedler数学的工作。QA/0212258。我们还描述了解决方案来自三重Massey产品在派生类别的相干层周期的投影线。
We show that a nondegenerate unitary solution $r(u,v)$ of the associative Yang-Baxter equation (AYBE) for $\Mat(N,\C)$ (see math.AG/0008156) with the Laurent series at $u=0$ of the form $r(u,v)=\frac{1\ot 1}{u}+r_0(v)+...$ satisfies the quantum Yang-Baxter equation, provided the projection of $r_0(v)$ to traceless matrices has a period. We classify all such solutions of the AYBE extending the work of Schedler math.QA/0212258. We also characterize solutions coming from triple Massey products in the derived category of coherent sheaves on cycles of projective lines.