Double Ore Extensions versus Iterated Ore Extensions

TL;DR

This paper investigates when double Ore extensions can be expressed as iterated Ore extensions, providing criteria and partial answers to existing questions in the algebraic structure of these extensions.

Contribution

It characterizes conditions under which double Ore extensions are equivalent to iterated Ore extensions, advancing understanding of their structural relationships.

Findings

Identifies criteria for double Ore extensions to be iterated Ore extensions

Provides partial answers to open questions in Zhang and Zhang (2008)

Enhances the classification of algebra extensions in noncommutative algebra

Abstract

Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J. Zhang and J. Zhang (2008) introduced an algebra extension $A_P[y_1,y_2;\sigma,\delta,\tau]$ of $A$, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over $A$. The aim of this paper is to describe those double Ore extensions which can be presented as iterated Ore extensions of the form $A[y_1;\sigma_1, \delta_1][y_2;\sigma_2, \delta_2]$. We also give partial answers to some questions posed in Zhang and Zhang (2008).