  We study the ozone group of noetherian Artin--Schelter regular algebras
satisfying a polynomial identity (or PI for short). The ozone group was shown
in previous work by the authors to be an important invariant in the study of PI
skew polynomial rings and their centers. In this paper, we show that skew
polynomial rings are in fact characterized as those algebras with maximal rank
ozone groups. We also classify those with trivial ozone groups, which must
necessarily be Calabi--Yau. This class includes most three-dimensional PI
Sklyanin algebras. Further examples and applications are given, including
applications to the Zariski Cancellation Problem.
