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

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