Complete classification of a class of $3$-dimensional algebras

TL;DR

This paper provides a comprehensive classification of a specific class of 3-dimensional algebras, showing that in algebraically closed fields, this class forms an open and dense subset in a 27-dimensional space.

Contribution

It offers a complete classification of a certain class of 3-dimensional algebras, expanding understanding of their structure and properties.

Findings

The classified class is an open, dense subset in 7-dimensional space.

The classification is complete for algebraically closed fields.

The class's structure is well-understood within the Zariski topology.

Abstract

A complete classification of a class of $3$-dimensional algebras is provided. In algebraically closed field $\mathbb{F}$ case this class is an open, dense (in Zariski topology) subset of $\mathbb{F}^{27}$.