Classification of affine prime regular Hopf algebras of GK-dimension one
Jinyong Wu, Gongxiang Liu, Nanqing Ding
TL;DR
This paper completes the classification of affine prime regular Hopf algebras of GK-dimension one, providing new insights and answering open questions about their structure and properties.
Contribution
It fully classifies these Hopf algebras and demonstrates the existence of non-pointed examples, addressing open problems in the field.
Findings
Negative answer to Brown-Zhang open question
Existence of prime regular Hopf algebras of GK-dimension one that are not pointed
Complete classification of affine prime regular Hopf algebras of GK-dimension one
Abstract
The classification of affine prime regular Hopf algebras of GK-dimension one is completed. As consequences, 1) we give a negative answer to an open question posed by Brown-Zhang and 2) we show that there do exist prime regular Hopf algebras of GK-dimension one which are not pointed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras