On Hopf algebras with positive bases
Quantum Algebra
2007-05-23 v1 Rings and Algebras
Abstract
We show that if a finite dimensional Hopf algebra over has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group and a factorization into two subgroups. We also show that Hopf algebras in the category of finite sets with correspondences as morphisms are classified in the similar way. Our results can be used to explain some results in Hopf algebras from set-theoretical viewpoint.
Cite
@article{arxiv.math/9911091,
title = {On Hopf algebras with positive bases},
author = {J. H. Lu and M. Yan and Y. C. Zhu},
journal= {arXiv preprint arXiv:math/9911091},
year = {2007}
}