Let A be a Koszul Artin-Schelter regular algebra, σ a graded automorphism of A and δ a degree-one σ-derivation of A. We introduce an invariant for δ called the σ-divergence of δ. We describe the Nakayama automorphism of the graded Ore extension $B=A[z;\sigma ,\delta ]$ explicitly using the σ-divergence of δ, and construct a twisted superpotential $\hat{\omega }$ for B so that it is a derivation quotient algebra defined by $\hat{\omega }$. We also determine all graded Ore extensions of noetherian Artin-Schelter regular algebras of dimension 2 and compute their Nakayama automorphisms.

中文翻译：

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Koszul Artin-Schelter正则代数的分级矿石扩展的Nakayama自同构

让一个是Koszul阿廷，Schelter正规代数，σ的分级构一个与δ学位，一个σ的-derivation一个。我们引入了一个不变δ称为σ的-divergence δ。我们描述了分级矿石扩展的中山自同构$乙=\mathrm{一个}[ž;\sigma ，\delta ]$明确地使用δ的σ-散度，构造一个扭曲的超电势$\hat{\omega }$对于B，因此它是由$\hat{\omega }$。我们还确定维数为2的Noetherian Artin-Schelter正则代数的所有渐变Ore扩展，并计算其Nakayama自同构。