Koszulity for graded skew PBW extensions

TL;DR

This paper investigates conditions under which graded skew PBW extensions over fields are Koszul, establishing that if the base algebra is Koszul, then the extension retains this property, thus expanding understanding of algebraic structures.

Contribution

It introduces graded skew PBW extensions and proves that these extensions are Koszul when the base algebra is Koszul, providing new insights into their algebraic properties.

Findings

Graded skew PBW extensions over fields can be Koszul if the base algebra is Koszul.

Established conditions for skew PBW extensions to be homogeneous pre-Koszul or Koszul.

Proved that finite presented Koszul algebras lead to Koszul graded skew PBW extensions.

Abstract

Pre-Koszul and Koszul algebras were defined by Priddy. There exist some relations between these algebras and the skew PBW extensions defined. We have established conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul K-algebra then every graded skew PBW extension of R is Koszul.