2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229432We 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.Rings and AlgebrasQuantum Algebra16A39, 16K40, 16E10, 16W50text