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Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras

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 $B=A[z;σ,δ]$ explicitly using the $σ$-divergence of $δ$, and construct a twisted superpotential $\hatω$ for $B$ so that it is a derivation quotient algebra defined by $\hatω$. We also determine all graded Ore extensions of noetherian Artin-Schelter regular algebras of dimension 2 and compute their Nakayama automorphisms.