Classifying bicrossed products of two Taft algebras

Abstract

We classify all Hopf algebras which factorize through two Taft algebras ${\mathbb{T}}_{n^2}(\bar{q})$ and respectively $T_{m^2}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\bar{q}\ne q^{n-1}$ then the matched pairs are in bijection with the group of $d$-th roots of unity in $k$, where $d=(m,n)$ while if $\bar{q}=q^{n-1}$ then besides the matched pairs above we obtain an additional family of matched pairs indexed by $k^{\ast }$. The corresponding bicrossed products (double cross product in Majid's terminology) are explicitly described by generators and relations and classified. As a consequence of our approach, we are able to compute the number of isomorphism types of these bicrossed products as well as to describe their automorphism groups.

Continues arXiv:1205.6110, arXiv:1205.6564; restates preliminaries and definitions for sake of clarity. Final version, to appear in J. Pure Appl. Algebra

Cited by in corpus (1)

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