  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.
