Finite dimensional pointed Hopf algebras over S_4

Abstract

Let k be an algebraically closed field of characteristic 0. We conclude the classification of finite dimensional pointed Hopf algebras whose group of group-likes is S_4. We also describe all pointed Hopf algebras over S_5 whose infinitesimal braiding is associated to the rack of transpositions.

22 pages. Some results extended

References in corpus (1)

• On pointed Hopf algebras associated to unmixed conjugacy classes in S_n

Cited by in corpus (11)

• Nichols algebras of group type with many quadratic relations
• On pointed Hopf algebras over dihedral groups
• Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
• Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$
• Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
• Deformation by cocycles of pointed Hopf algebras over non-abelian groups
• Finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}$ of Kashina
• Copointed Hopf algebras over ${\mathbb{S}}_4$
• On some classification of finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}^{\ast }$ of Kashina
• On Hopf algebras whose coradical is a cocentral abelian cleft extension
• Twist equivalence for Nichols algebras over Coxeter groups