We compute necessary conditions on Yetter-Drinfeld modules over the groups PGL(2,q)=PGL(2,\FFq) and PSL(2,q)=PSL(2,\FFq) 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 M20 and M21=PSL(3,4).
@article{arxiv.0802.2567,
title = {On Nichols algebras over PGL(2,q) and PSL(2,q)},
author = {S. Freyre and M. Graña and L. Vendramin},
journal= {arXiv preprint arXiv:0802.2567},
year = {2010}
}