Differential smoothness of affine Hopf algebras of Gelfand-Kirillov   dimension two
  Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth. 
Tomasz Brzezi\'nski
math.RA