Koszulity for skew PBW extensions over fields

TL;DR

This paper establishes conditions under which skew PBW extensions over fields are Koszul or homogeneous Koszul, and shows that constant skew PBW extensions are PBW deformations of their homogeneous counterparts.

Contribution

It provides new criteria for Koszulity in skew PBW extensions over fields and links constant skew PBW extensions to PBW deformations.

Findings

Conditions for skew PBW extensions to be Koszul or homogeneous Koszul.

Constant skew PBW extensions are PBW deformations of their homogeneous versions.

Connections between skew PBW extensions and classical Koszul algebra theory.

Abstract

Koszul and homogeneous Koszul algebras were defined by Priddy in \cite{Priddy1970}. There exist some relations between these algebras and the skew PBW extensions introduced in \cite{LezamaGallego}. In this paper we give conditions to guarantee that skew PBW extensions over fields are Koszul or homogeneous Koszul. We also show that a constant skew PBW extension of a field is a PBW deformation of its homogeneous version.