Deformation by cocycles of pointed Hopf algebras over non-abelian groups

Abstract

We introduce a method to construct explicitly multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V [circle times] V and give a close formula to deform braided commutator-type relations. Using this construction, we show that all known finite dimensional pointed Hopf algebras over the dihedral groups D[subscript m] with m = 4t [greater than or equal to] 12, over the symmetric group S[subscript 3] and some families over S[subscript 4] are cocycle deformations of bosonizations of Nichols algebras.