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

Abstract

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.

Postprint version: Minor changes in Table 1 of Theorem 1.1 and Corollary 3.5

References in corpus (1)

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

Cited by in corpus (7)

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• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(n,q) and PSp(2n,q)
• Twist equivalence for Nichols algebras over Coxeter groups