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arXiv · 2507.15252

Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations

Yan Cao·Yuan Shen·Xin Wang
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Abstract

Let $A$ be a Koszul Artin-Schelter regular algebra and $B=A_P[y_1,y_2;\varsigma,\nu]$ be a graded double Ore extension of $A$ where $\varsigma:A\to M_{2\times 2}(A)$ is a graded algebra homomorphism and $\nu:A\to A^{\oplus 2}$ is a degree one $\varsigma$-derivation. We construct a minimal free resolution for the trivial module of $B$, and it implies that $B$ is still Koszul. We introduce a homological invariant called $\varsigma$-divergence of $\nu$, and with its aid, we obtain a precise description of the Nakayama automorphism of $B$. A twisted superpotential $\hat{\omega}$ for $B$ with respect to the Nakayama automorphism is constructed so that $B$ is isomorphic to the derivation quotient algebra of $\hat{\omega}$.

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Yan Cao, Yuan Shen, Xin Wang. 2025-07-21. Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations. https://arxiv.org/abs/2507.15252

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