Discriminants of Taft algebra smash products and applications

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.