Bicrossed products with the Taft algebra

Abstract

Let $G$ be a group which admits a generating set consisting of finite order elements. We prove that any Hopf algebra which factorizes through the Taft algebra and the group Hopf algebra $K[G]$ (equivalently, any bicrossed product between the aforementioned Hopf algebras) is isomorphic to a smash product between the same two Hopf algebras. The classification of these smash products is shown to be strongly linked to the problem of describing the group automorphisms of $G$. As an application, we completely describe by generators and relations and classify all bicrossed products between the Taft algebra and the group Hopf algebra $K[D_{2n}]$, where $D_{2n}$ denotes the dihedral group.

Continues arXiv:1205.6110, arXiv:1205.6564, arXiv:1603.01854, arXiv:1611.05674; restates preliminaries and definitions for sake of clarity

References in corpus (1)

• Hopf Algebras which Factorize through the Taft Algebra $T_{m^2}(q)$ and the Group Hopf Algebra $K[C_n]$