Prime regular Hopf Algebras of GK-dimension One
K.A. Brown, J.J. Zhang
TL;DR
This paper classifies affine prime regular Hopf algebras of GK-dimension one over an algebraically closed field, providing properties, examples, and a complete list for prime PI-degree cases.
Contribution
It offers the first classification of such Hopf algebras, detailing their properties, examples, and a complete list under prime PI-degree conditions.
Findings
Properties of affine prime regular Hopf algebras of GK-dimension one
Examples of such Hopf algebras
Complete classification when PI-degree is prime
Abstract
This paper constitutes the first part of a program to classify all affine prime regular Hopf algebras of Gelfand-Kirillov dimension one over an algebraically closed field of characteristic zero. We prove a number of properties of such an algebra, list some classes of examples, and then prove that - when the PI-degree of is prime - our list contains all such algebras.
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