Hopf algebras of GK-dimension two with vanishing Ext-group
  We construct and study a family of finitely generated Hopf algebra domains $H$ of Gelfand-Kirillov dimension two such that $\Ext^1_H(k,k)=0$. Consequently, we answer a question of Goodearl and the second-named author. 
D.-G. Wang, J.J. Zhang and G. Zhuang
math.RA