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arXiv · 1506.06794

Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL(n,q)

Nicolás Andruskiewitsch·Giovanna Carnovale·Gastón Andrés García
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Abstract

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to semisimple orbits, have infinite dimension. We introduce a new criterium to determine when a conjugacy class collapses and prove that for infinitely many pairs (n,q), any finite-dimensional pointed Hopf algebra H with G(H) = PSL(n,q) or SL(n,q) is isomorphic to a group algebra.

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Nicolás Andruskiewitsch, Giovanna Carnovale, Gastón Andrés García. 2018-03-12. Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL(n,q). https://doi.org/10.4171/rmi%2F961

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