关于PGL（2，q）和PSL（2，q）上的Nichols代数
On Nichols algebras over PGL(2,q) and PSL(2,q)
摘要：
我们计算了群$\mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q)$和$\mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q)$上的Yetter-Drinfeld模生成有限维Nichols代数的必要条件.这是第一步的分类点霍普夫代数组群同构于这些群体之一。作为这项工作中开发的技术的副产品，我们证明了在Mathieu群$M_{20}$和$M_{21}=\mathbf{PSL}(3,4)$上不存在非平凡的有限维点霍普夫代数。
英文摘要：
We compute necessary conditions on Yetter-Drinfeld modules over the groups $\mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q)$ and $\mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q)$ to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that there is no non-trivial finite-dimensional pointed Hopf algebra over the Mathieu groups $M_{20}$ and $M_{21}=\mathbf{PSL}(3,4)$.
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