On Hopf algebras with positive bases

Details On Hopf algebras with positive bases On Hopf algebras with positive bases

1999-11-13

arxiv.org/abs/math/9911091v1

Mathematics

Quantum Algebra

Scientific paper

We show that if a finite dimensional Hopf algebra over ${\bf C}$ has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group $G$ and a factorization $G=G_+G_-$ 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.

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