Hopf algebras with enough quotients

Abstract

A family of algebra maps $H\to A_i$ whose common domain is a Hopf algebra is said to be jointly inner faithful if it does not factor simultaneously through a proper Hopf quotient of $H$. We show that tensor and free products of jointly inner faithful maps of Hopf algebras are again jointly inner faithful, generalizing a number of results in the literature on torus generation of compact quantum groups.

8 pages + references

References in corpus (4)

• Kirchberg's Factorization Property for Discrete Quantum Groups
• A note on the half-liberation operation
• Compact quantum groups generated by their tori
• Unitary quantum groups vs quantum reflection groups