Graded Morita equivalences for generic Artin-Schelter regular algebras

Let A = A(E, sigma), A' = A(E', sigma') be Noetherian Artin-Schelter regular geometric algebras with dime(k) A(1) = dim(k) A(1)' = n, and let v, v' be generalized Nakayama automorphisms of A, A'. In this paper, we study relationships between the conditions (A) A is graded Morita equivalent to A', and (B) A(E, v*, sigma(n)) is isomorphic to A(E', (v)* (sigma')(n)) as graded algebras. It is proved that if A, A' are "generic" 3-dimensional quadratic Artin-Schelter regular algebras, then (A) is equivalent to (B), and if A, A' are n-dimensional skew polynomial algebras, then (A) implies (B).