PBW Extensions

The aim of this paper is to establish necessary and sufficient algorithmic conditions to guarantee that an algebra is actually a 3-dimensional skew polynomial algebra in the sense of Bell and Smith [1].

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 …