论文标题
二面体组的小量子基团的简单模块
Simple modules of small quantum groups at dihedral groups
论文作者
论文摘要
基于先前关于有限维尼科尔斯代数分类的结果，以及二二二二核的简单模块的表征，我们计算了有限型尼古拉斯$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d drinfeld双打的不可减至的特征。 $ t \ geq 3 $。为此，我们开发了可以在任何HOPF代数上应用于Nichols代数的新技术。也就是说，我们解释了当尼科尔斯代数由可分解的模块生成时，如何递归不可约的表示，并表明Verma模块中最小程度的最高重量最高重量决定了其SOCLE。我们还证明，刚性简单模块张开一个简单的模块给出了一个半神经模块。
Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups $\mathbb{D}_{4t}$ with $t\geq 3$. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively irreducible representations when the Nichols algebra is generated by a decomposable module, and show that the highest-weight of minimum degree in a Verma module determines its socle. We also prove that tensoring a simple module by a rigid simple module gives a semisimple module.
