PBW bases for some 3-dimensional skew polynomial algebras

TL;DR

This paper provides an algorithmic framework to determine when a 3-dimensional skew polynomial algebra, as defined by Bell and Smith, has a PBW basis, aiding classification and understanding of such algebras.

Contribution

It introduces necessary and sufficient conditions to identify PBW bases in 3-dimensional skew polynomial algebras, advancing algebraic classification methods.

Findings

Established criteria for PBW basis existence

Provided an algorithmic approach for classification

Enhanced understanding of 3D skew polynomial algebras

Abstract

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.