PreprintCC BY 4.0arXiv
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 TN,n,ξ and the Radford algebra R. If pnmid N, every matched pair is trivial, and the corresponding bicrossed product is the tensor product Hopf algebra. If p| N, matched pairs are parametrized by β∈𝔽p, 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.
Related
- Generalized free wreath products and their operator algebras
- Rigid and τ-locally free modules via Taft algebras
- Selfless reduced free products and graph products of C⁎-algebras
- Rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators
- Classification of reduced free products of nuclear C*-algebras
BibTeX
@misc{xiong2026bicrossed,
title = {{Bicrossed products of generalized Taft algebras and Radford algebras}},
author = {Rongchuan Xiong},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29536},
eprint = {2608.29536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bicrossed products of generalized Taft algebras and Radford algebras
AU - Rongchuan Xiong
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29536
UR - https://arxiv.org/abs/2608.29536
AB - 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 pnmid N, every matched pair is trivial, and the corresponding bicrossed product is the tensor product Hopf algebra. If p| N, matched pairs are parametrized by β∈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.
ER -