Finite dimensional Nichols algebras over certain p-groups

Abstract

ABSTRACTWe investigate pointed Hopf algebras over finite nilpotent groups of odd order, with nilpotency class 2. For such a group G, we show that if its commutator subgroup coincides with its center, then there exists no non-trivial finite-dimensional pointed Hopf algebra with kG as its coradical. We apply these results to non-abelian groups of order p3, p4 and p5, and list all the pointed Hopf algebras of order p6, whose group of grouplikes is non-abelian.