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 tensor 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_m with m=4t > 11, over the symmetric group S_3 and some families over S_4 are cocycle deformations of bosonizations of Nichols algebras.

20 pages. This version: extended version following the referee's suggestions. Intended for non-experts

References in corpus (5)

• Finite-dimensional pointed Hopf algebras with alternating groups are trivial
• On pointed Hopf algebras over dihedral groups
• Finite dimensional pointed Hopf algebras over S_4
• On pointed Hopf algebras associated with alternating and dihedral groups
• Pointed Hopf algebras as cocycle deformations

Cited by in corpus (4)

• On finite-dimensional copointed Hopf algebras over dihedral groups
• Copointed Hopf algebras over ${\mathbb{S}}_4$
• Finite-dimensional Nichols algebras over dual Radford algebras
• Multiparameter quantum groups, bosonizations and cocycle deformations