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

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to non-semisimple orbits, have infinite dimension. We spell out a new criterium to show that a rack collapses.