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

• Nicolás Andruskiewitsch ^[1] ; Giovanna Carnovale ^[2] ; Gastón Andrés García ^[3]
  1. [1] Universidad Nacional de Córdoba

     Universidad Nacional de Córdoba

     Argentina

     
  2. [2] University of Padua

     University of Padua

     Padova, Italia

     
  3. [3] Universidad Nacional de La Plata

     Universidad Nacional de La Plata

     Argentina

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 3, 2017 (Ejemplar dedicado a: Yves Meyer), págs. 995-1024
• Idioma: inglés
• DOI: 10.4171/RMI/961
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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)≃PSLn(q) or SLn(q) is isomorphic to a group algebra.