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

Abstract

We explore a method for explicitly constructing 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 V and give a formula for deforming braidedcommutator-type relations. Using this construction, we show that all known finite-dimensional pointed Hopf algebras over the dihedral groups D m with m = 4t 12, over the symmetric group S 3 , and some families over S 4 are cocycle deformations of bosonizations of Nichols algebras.