  PBW deformations of Artin-Schelter regular algebras are skew Calabi-Yau. We
prove that the Nakayama automorphisms of such PBW deformations can be obtained
from their homogenizations. Some Calabi-Yau properties are generalized without
Koszul assumption. We also show that the Nakayama automorphisms of such PBW
deformations control Hopf actions on them.
