Double Ore Extensions

TL;DR

This paper introduces double Ore extensions as a generalization of Ore extensions, proves their regularity properties when applied to Artin-Schelter regular algebras, and explores their basic properties, laying groundwork for constructing new regular algebras.

Contribution

It establishes that connected graded double Ore extensions of Artin-Schelter regular algebras are also Artin-Schelter regular, and studies fundamental properties like the determinant of DE-data.

Findings

Proved double Ore extensions preserve Artin-Schelter regularity.

Analyzed properties such as the determinant of DE-data.

Constructed 26 families of regular algebras in a sequel paper.

Abstract

A double Ore extension is a natural generalization of the Ore extension. We prove that a connected graded double Ore extension of an Artin-Schelter regular algebra is Artin-Schelter regular. Some other basic properties such as the determinant of the DE-data are studied. Using the double Ore extension, we construct 26 families of Artin-Schelter regular algebras of global dimension four in a sequel paper.