Abstract

SUAREZ, HÉCTOR; LEZAMA, OSWALDO  and  REYES, ARMANDO. Calabi-Yau property for graded skew PBW extensions. Rev.colomb.mat. [online]. 2017, vol.51, n.2, pp.221-239. ISSN 0034-7426.

Graded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition for this kind of extensions. We prove that every graded quasi-commutative skew PBW extension of an Artin-Schelter regular algebra is also an Artin-Schelter regular algebra and, as a consequence, every graded quasi-commutative skew PBW extension of a connected skew Calabi-Yau algebra is skew Calabi-Yau. Finally, we prove that graded skew PBW extensions of a finitely presented connected Auslander-regular algebra are skew Calabi-Yau.

Keywords : Graded skew PBW extensions; AS-regular algebras; skew Calabi-Yau algebras.

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