A classification of relation types of Ore extensions of dimension 5

TL;DR

This paper classifies relation types of Ore extensions of dimension 5, providing a structural understanding and linking known algebra types to Ore extensions, with insights into their realization as enveloping algebras.

Contribution

It offers a comprehensive classification of relation types for dimension 5 Ore extensions and explores their realization as known algebraic structures.

Findings

Every known algebra of dimension 5 can be realized as an Ore extension.

The structure of relations and resolutions for extensions with 3 and 4 generators is characterized.

Some algebra types cannot be realized as enveloping algebras.

Abstract

In order to study AS-regular algebras of dimension 5, we consider dimension 5 graded iterated Ore extensions generated in degree one. We classify the possible degrees of relations and structure of the free resolution for extensions with 3 and 4 generators. We show that every known type of algebra of dimension 5 can be realized by an Ore extension and we consider which of these types cannot be realized by an enveloping algebra.