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

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