The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations - Shen, Yuan; Guo, Yang (Comptes Rendus. Mathématique, 2022)
Let $A$ be a noncommutative Artin–Schelter regular algebra of dimension $2$ with the Nakayama automorphism $\mu _A$ and $U$ a PBW deformation of $A$ with the Nakayama automorphism $\mu _U$. We prove that any graded Ore extension $A[z;\mu _A,\delta ]$ and any filtered Ore extension $U[z;\mu _U,\tilde{\delta }]$ are $3$-Calabi–Yau.