JournalsrmiVol. 33, No. 3pp. 995–1024

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

  • Nicolás Andruskiewitsch

    Universidad Nacional de Córdoba, Argentina
  • Giovanna Carnovale

    Università degli Studi di Padova, Italy
  • Gastón Andrés García

    Universidad Nacional de La Plata, Argentina
Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL$_n(q)$ cover

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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)(n,q), any finite-dimensional pointed Hopf algebra HH with G(H)PSLn(q)G(H)\simeq\mathbf {PSL}_{n}(q) or SLn(q)\mathbf {SL}_{n}(q) is isomorphic to a group algebra.

Cite this article

Nicolás Andruskiewitsch, Giovanna Carnovale, Gastón Andrés García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSLn(q)_n(q). Rev. Mat. Iberoam. 33 (2017), no. 3, pp. 995–1024

DOI 10.4171/RMI/961