Degenerations of 8-dimensional 2-step nilpotent Lie algebras

TL;DR

This paper classifies degenerations of 8-dimensional 2-step nilpotent Lie algebras over complex numbers, providing a geometric understanding of their structure and relationships.

Contribution

It offers the first comprehensive geometric classification of the variety of 8-dimensional 2-step nilpotent Lie algebras, detailing their degeneration patterns.

Findings

Complete classification of degenerations within the variety.

Identification of geometric structures governing these degenerations.

Insights into the algebraic and geometric properties of 8-dimensional 2-step nilpotent Lie algebras.

Abstract

In this work, we consider degenerations between 8-dimensional 2-step nilpotent Lie algebras over $\mathbb{C}$ and obtain the geometric classification of the variety $\mathcal{N}^2_8$.