Year: 2026
Type: preprint
Abstract: Over an algebraically closed field of characteristic $p>0$, we classify all matched pairs between a generalized Taft algebra $T_{N,n,ξ}$ 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 $β\in\mathbb F_p$, 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.
Source: arXiv (Cornell University)
Author: Xiong, Rongchuan
Institution: Changzhou University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204884697