Homogenized skew PBW extensions

Abstract

Abstract In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of $$\sigma $$ σ -filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a $$\sigma $$ σ -filtered skew PBW extension A over a ring R is a graded skew PBW extension over the homogenization of R. Using this fact, we prove that if the homogenization of R is Auslander-regular, then the homogenization of A is a domain Noetherian, Artin–Schelter regular, and A is Noetherian, Zariski and (ungraded) skew Calabi–Yau.

Keywords

• 16S36
• 16S37
• 16W50
• 16W70
• 13N10