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, Tome 360 (2022) no. G7, pp. 739-749.

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.

Classification : 16S36, 16S37, 16S38, 16S80, 16E65

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