A skew Calabi-Yau algebra A is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We develop formulas for the Nakayama automorphisms of other algebras derived from A by important constructions: (1) smash product algebras A#H for a Hopf algebras H acting on A, and (2) graded twists of A. We discuss applications of these formulas and open questions.
This is joint work with Manny Reyes and James Zhang.