Deformations of Four Dimensional Lie Algebras

TL;DR

This paper explores the deformation theory of four-dimensional Lie algebras, revealing a geometric orbifold structure of their moduli space and providing insights into how these algebras vary within this space.

Contribution

It offers a detailed analysis of the versal deformations of four-dimensional Lie algebras and describes the moduli space as a geometric orbifold with few exceptions.

Findings

Moduli space has an orbifold structure

Deformations are classified and visualized geometrically

Few exceptional points in the moduli space

Abstract

We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is assembled. Surprisingly, we get a nice geometric description of this moduli space essentially as an orbifold, with just a few exceptional points.