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

Nicolás Andruskiewitsch, Giovanna Carnovale, Gaston Andrés García

• 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.