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 1H(k,k)≠ 0. The latter condition is conjecturally redundant, as no examples are known (among noetherian Hopf algebra domains of GK-dimension two) where it fails.
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