The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations

Abstract

Let A be a noncommutative Artin–Schelter regular algebra of dimension 2 with the Nakayama automorphism μ A and U a PBW deformation of A with the Nakayama automorphism μ U . We prove that any graded Ore extension A[z;μ A ,δ] and any filtered Ore extension U[z;μ U ,δ ˜] are 3-Calabi–Yau.