Nakayama automorphisms of double Ore extensions of Koszul regular algebras

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• 作者：Can Zhu ; Fred Van Oystaeyen ; Yinhuo Zhang
• 关键词：Mathematics Subject ClassificationPrimary 16E65 ; 16S36 ; 16U20
• 刊名：manuscripta mathematica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：152
• 期：3-4
• 页码：555-584
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1785
• 卷排序：152

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.