Bicrossed products of generalized Taft algebras and Radford algebras

Abstract

Over an algebraically closed field of characteristic $p>0$, we classify all matched pairs between a generalized Taft algebra $T_{N,n,\xi }$ and the Radford algebra $R$. If $p\nmid N$, every matched pair is trivial, and the corresponding bicrossed product is the tensor product Hopf algebra. If $p\mid N$, matched pairs are parametrized by $\beta \in {\mathbb{F}}_p$, and the bicrossed products are described by explicit cross relations. Two such bicrossed products are isomorphic as Hopf algebras if and only if their parameters are equal; hence there are exactly $p$ isomorphism classes in this case.