On degenerations of algebras over an arbitrary field

TL;DR

This paper classifies all n-dimensional algebras over an infinite field that have the property that their only proper degeneration is the abelian Lie algebra, providing a comprehensive understanding of their degeneration behavior.

Contribution

It offers a complete classification of such algebras over arbitrary infinite fields, extending previous results to a broader context.

Findings

Identified all n-dimensional algebras with unique degeneration to abelian Lie algebra.

Extended classification to arbitrary infinite fields.

Provided structural insights into algebra degenerations.

Abstract

For each $n\ge2$ we classify all $n$-dimensional algebras over an arbitrary infinite field which have the property that the $n$-dimensional abelian Lie algebra is their only proper degeneration.