A classification result on prime Hopf algebras of GK-dimension one

Abstract

In this paper, we classify all prime Hopf algebras $H$ of GK-dimension one satisfying the following two conditions: 1) $H$ has a 1-dimensional representation of order PI.deg$(H)$ and 2) the invariant components of $H$ with respect to this 1-dimensional representation are domains (see Section 2 for related definitions). As consequences, 1) a number of new Hopf algebras of GK-dimension one are found and some of them are not pointed, 2) we give a partial answer to a question posed by Brown and Zhang and 3) some new kinds of finite-dimensional Hopf algebras are found.

92 pages. In page 2, the graph should be "cusp ${\in }_{Z_6}^{{\mathbb{Z}}_6}\mathcal{YD}$ ". Your comments are very welcome! Comparing with the first version, some typos were corrected

References in corpus (1)

• Prime regular Hopf Algebras of GK-dimension One

Cited by in corpus (2)

• Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type
• The nodal cubic and quantum groups at roots of unity