On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Abstract

Homological smoothness and twisted Calabi–Yau property of generalized Weyl algebras over polynomial algebras in two variables is studied. A necessary and sufficient condition to be homologically smooth is given. The Nakayama automorphisms of such algebras are also computed in terms of the Jacobian determinants of defining automorphisms.