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

Let A be a Koszul Artin-Schelter regular algebra, sigma a graded automorphism of A and delta a degree-one sigma-derivation of A. We introduce an invariant for delta called the sigma-divergence of delta. We describe the Nakayama automorphism of the graded Ore extension B= A[z, sigma, delta] explicitly using the sigma-divergence of d, and construct a twisted superpotential (omega) over cap for B so that it is a derivation quotient algebra defined by (omega) over cap. We also determine all graded Ore extensions of noetherian Artin-Schelter regular algebras of dimension 2 and compute their Nakayama automorphisms. (C) 2021 Elsevier Inc. All rights reserved.