Abstract
Let A=A(E,σ),A'=A(E',σ') be Noetherian Artin-Schelter regular geometric algebras with dimkA1=dimkA1'=n, and let ν,ν' 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,ν∗σn) is isomorphic to A(E',(ν')∗(σ')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).
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