Double Extension Regular Algebras of Type (14641)

TL;DR

This paper constructs new families of Artin-Schelter regular algebras of dimension four using double Ore extensions, demonstrating their desirable algebraic properties and novelty over previous classifications.

Contribution

It introduces several new Artin-Schelter regular algebras of global dimension four via double Ore extensions, expanding the known classes of such algebras.

Findings

All constructed algebras are strongly noetherian, Auslander regular, Koszul, and Cohen-Macaulay domains.

Many of these algebras are new and not isomorphic to known extensions of dimension three.

The paper provides explicit constructions and proofs of properties for these algebras.

Abstract

We construct several families of Artin-Schelter regular algebras of global dimension four using double Ore extension and then prove that all these algebras are strongly noetherian, Auslander regular, Koszul and Cohen-Macaulay domains. Many regular algebras constructed in the paper are new and are not isomorphic to either a normal extension or an Ore extension of an Artin-Schelter regular algebra of global dimension three.