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

The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations

“…In fact, these two results do not occur incidentally. In this note, we make a step further to show the same conclusion in [18] holds without the noetherian assumption.…”

“…, n + 1 and x n+1 = z. There is an explicit description of the superpotential for B which is a generalization of [10, Theorem 0.1 (ii)] and a special case of [18,Theorem 3.11].…”

“…Many known 3-Calabi-Yau algebras can be constructed by Ore extensions (see [1,5,9,10,18,20]). Actually, this fact is due to the twisted Calabi-Yau (also called skew Calabi-Yau) property, which is a generalization of the Calabi-Yau property, is preserved and may be untwisted under Ore extensions (see [7,12]).…”

“…So there is a natural question what role of the µ Aderivation δ plays in the construction of Calabi-Yau algebras by Ore extensions. Recently, the papers [11,18,21] made contribution to this problem in abstract terms.…”

“…He, Van Oystaeyen and Zhang in [10] showed that graded Ore extensions of graded 2-Calabi-Yau algebras are graded 3-Calabi-Yau if the values of the generating relation acting by derivations vanish. The authors in [18] showed that the µ A -derivation does not make any influence on the graded Ore extensions of noncommutative noetherian AS-regular algebras of dimension 2 being graded 3-Calabi-Yau. In fact, these two results do not occur incidentally.…”