A generalized Koszul property for skew PBW extensions

TL;DR

This paper proves that certain algebraic extensions called skew PBW extensions preserve the generalized Koszul property of the base algebra R, especially under semi-commutative and augmented conditions.

Contribution

It establishes that constant skew PBW extensions of a generalized Koszul algebra are also generalized Koszul, extending the class of algebras with this property.

Findings

Constant skew PBW extensions preserve the generalized Koszul property.

Semi-commutative skew PBW extensions of augmented Koszul algebras are also augmented Koszul.

The results apply to a broad class of algebraic extensions.

Abstract

Let R be a commutative algebra. In this paper we show that constant skew PBW extensions of a generalized Koszul algebra R are also generalized Koszul. Let A be a semi-commutative skew PBW extension of R such that A is R-augmented. We show also that if R is augmented Koszul then A is R-augmented Koszul.