# Degenerations of nilpotent algebras

## TL;DR

This paper provides a comprehensive classification of degenerations of low-dimensional nilpotent algebras over complex numbers, correcting previous errors and covering various algebra types.

## Contribution

It offers a complete description of degenerations for specific classes of nilpotent algebras, improving upon prior incomplete or incorrect classifications.

## Key findings

- Complete classification of 3D nilpotent algebra degenerations
- Classification of 4D nilpotent commutative algebra degenerations
- Classification of 5D nilpotent anticommutative algebra degenerations

## Abstract

We give a complete description of degenerations of $3$-dimensional nilpotent algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional nilpotent anticommutative algebras over $ \mathbb C$. In particular, we correct several mistakes from the paper `Contractions of low-dimensional nilpotent Jordan algebras' by Ancochea Berm\'{u}dez, Fres\'{a}n and Margalef Bentabol.