Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two

Abstract

We classify all noetherian Hopf algebras $H$ over an algebraically closed field $k$ of characteristic zero which are integral domains of Gelfand-Kirillov dimension two and satisfy the condition $\Ext^1_H(k,k)\neq 0$. The latter condition is conjecturally redundant, as no examples are known (among noetherian Hopf algebra domains of GK-dimension two) where it fails.

References in corpus (1)

• Prime regular Hopf Algebras of GK-dimension One

Cited by in corpus (5)

• The Dixmier-Moeglin equivalence for cocommutative Hopf algebras of finite Gelfand-Kirillov dimension
• Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic
• Connected Hopf algebras and iterated Ore extensions
• Universal enveloping algebras of Poisson Hopf algebras
• Locally Finite Representations Over Noetherian Hopf algebras