A note on split extensions of bialgebras
Rings and Algebras
2018-09-27 v2 Category Theory
Abstract
We prove a universal characterization of Hopf algebras among cocommutative bialgebras over a field: a cocommutative bialgebra is a Hopf algebra precisely when every split extension over it admits a join decomposition. We also explain why this result cannot be extended to a non-cocommutative setting.
Cite
@article{arxiv.1701.00665,
title = {A note on split extensions of bialgebras},
author = {Xabier García-Martínez and Tim Van der Linden},
journal= {arXiv preprint arXiv:1701.00665},
year = {2018}
}
Comments
Reduced the context to algebraically closed fields