Nakayama automorphisms of double Ore extensions of Koszul regular algebras

Abstract

Let A be a Koszul Artin–Schelter regular algebra and σσ an algebra homomorphism from A to M2×2(A)M2×2(A). We compute the Nakayama automorphisms of a trimmed double Ore extension AP[y1,y2;σ]AP[y1,y2;σ] [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;θ]A[t;θ] , where θθ is a graded algebra automorphism of A. These lead to a characterization of the Calabi–Yau property of AP[y1,y2;σ]AP[y1,y2;σ] , the skew Laurent extension A[t±1;θ]A[t±1;θ] and A[y±11,y±12;σ]A[y1±1,y2±1;σ] with σσ a diagonal type.