  This is a continuation of the authors' study of finite-dimensional pointed
Hopf algebras H which act inner faithfully on commutative domains. As mentioned
in Part I of this work, the study boils down to the case where H acts inner
faithfully on a field. These Hopf algebras are referred to as
Galois-theoretical.
  In this work, we provide classification results for finite-dimensional
pointed Galois-theoretical Hopf algebras H of finite Cartan type. Namely, we
determine when such H of type A_1^{\times r} and some H of rank two possess the
Galois-theoretical property. Moreover, we provide necessary and sufficient
conditions for Reshetikhin twists of small quantum groups to be
Galois-theoretical.
