A classification result on prime Hopf algebras of GK-dimension one
Quantum Algebra
2020-01-07 v2
Abstract
In this paper, we classify all prime Hopf algebras of GK-dimension one satisfying the following two conditions: 1) has a 1-dimensional representation of order PI.deg and 2) the invariant components of 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.
Keywords
Cite
@article{arxiv.1804.08973,
title = {A classification result on prime Hopf algebras of GK-dimension one},
author = {Gongxiang Liu},
journal= {arXiv preprint arXiv:1804.08973},
year = {2020}
}
Comments
92 pages. In page 2, the graph should be "cusp $\in ^{\Z_6}_{Z_6}\mathcal{YD}$ ". Your comments are very welcome! Comparing with the first version, some typos were corrected