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arXiv · 0802.2567

On Nichols algebras over PGL(2,q) and PSL(2,q)

S. Freyre·M. Graña·L. Vendramin
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Abstract

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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S. Freyre, M. Graña, L. Vendramin. 2009-03-23. On Nichols algebras over PGL(2,q) and PSL(2,q). https://doi.org/10.1142/s0219498810003823

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