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

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

2008-02-19

arxiv.org/abs/0802.2567v3

J. Algebra Appl., Vol. 9, No. 2 (2010) 195-208

Mathematics

Quantum Algebra

Minor changes

Scientific paper

10.1142/S0219498810003823

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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