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arXiv · 1401.0330

Nakayama automorphisms of double Ore extensions of Koszul regular algebras

Can Zhu·Fred Van Oystaeyen·Yinhuo Zhang
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Abstract

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 \cite{ZZ08}). 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.

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Can Zhu, Fred Van Oystaeyen, Yinhuo Zhang. 2014-01-01. Nakayama automorphisms of double Ore extensions of Koszul regular algebras. https://arxiv.org/abs/1401.0330

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