The classification of algebras of level one

TL;DR

This paper classifies all complex finite-dimensional algebras of level one, identifying a list of representative algebras such that their closures encompass all algebras of this type.

Contribution

It provides a complete classification of level one algebras up to isomorphism, filling a gap in the understanding of algebra degenerations.

Findings

Identified all level one algebras up to isomorphism

Established the closure relations among these algebras

Provided a comprehensive list of representative algebras

Abstract

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.