参数化杨-巴克斯特方程解的量子群
Quantum groups obtained from solutions to the parametrized Yang-Baxter equation
摘要：
在这篇文章中，我们使用FRT构造的参数化版本，构造两个新的余拟三角霍普夫代数。第一个，$\widehat{SL_q(2)}$，是仿射$SL(2)$上坐标环的量子化。我们表明，有一个二元关系，这个对象和更知名的$U_q(\widehat{\mathfrak{sl}_2})$。然后，我们建立某些不可约余模的这个Hopf代数，并证明了一个不可约准则，其张量积的精神的Chari和Pressley。第二个目标是建立从一个解决方案的参数化杨-巴克斯特方程与参数组$GL(2, \mathbb{C}) \times GL (1,\mathbb{C})$。这个解并不来自任何已知的量子群，尽管它与来自$U_{\pm i}(\widehat{\mathfrak{sl}_2})$和$U_q(\widehat{\mathfrak{gl}(1|1)})$的两个解都相关。然后，我们研究某些不可约余模这个新建成的对象。
英文摘要：
In this article we use a parametrized version of the FRT construction to construct two new coquasitriangular Hopf algebras. The first one, $\widehat{SL_q(2)}$, is a quantization of the coordinate ring on affine $SL(2)$. We show that there is a duality relation between this object and the more well-known $U_q(\widehat{\mathfrak{sl}_2})$. We then build certain irreducible comodules of this Hopf algebra and prove an irreducibility criterion for their tensor product in the spirit of Chari and Pressley. The second object is built from a solution of the parametrized Yang-Baxter equation with parameter group $GL(2, \mathbb{C}) \times GL (1,\mathbb{C})$. This solution doesn't come from any known quantum group, though it is related to both solutions coming from $U_{\pm i}(\widehat{\mathfrak{sl}_2})$ and $U_q(\widehat{\mathfrak{gl}(1|1)})$. We then study certain irreducible comodules of this newly built object.
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