English

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

Quantum Algebra 2010-07-26 v3

Abstract

We compute necessary conditions on Yetter-Drinfeld modules over the groups PGL(2,q)=PGL(2,\FFq)\mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q) and PSL(2,q)=PSL(2,\FFq)\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 M20M_{20} and M21=PSL(3,4)M_{21}=\mathbf{PSL}(3,4).

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Cite

@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}
}

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