文摘
Let A be a Koszul Artin–Schelter regular algebra and \(\sigma \) an algebra homomorphism from A to \(M_{2\times 2}(A)\). We compute the Nakayama automorphisms of a trimmed double Ore extension \(A_P[y_1, y_2; \sigma ]\) [introduced in Zhang and Zhang (J Pure Appl Algebra 212:2668–2690, 2008)]. Using a similar method, we also obtain the Nakayama automorphism of a skew polynomial extension \(A[t; \theta ]\), where \(\theta \) is a graded algebra automorphism of A. These lead to a characterization of the Calabi–Yau property of \(A_P[y_1, y_2; \sigma ]\), the skew Laurent extension \(A[t^{\pm 1}; \theta ]\) and \(A[y_1^{\pm 1}, y_2^{\pm 1}; \sigma ]\) with \(\sigma \) a diagonal type.