Homogenized skew PBW extensions


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 $\sigma$-filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a $\sigma$-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.

Arabian Journal of Mathematics, 12, 247-263. doi:10.1007/s40065-022-00410-z