Moduli spaces of low dimensional Lie superalgebras

TL;DR

This paper explores the structure of moduli spaces for low-dimensional complex Lie superalgebras, revealing a stratification pattern similar to that of ordinary Lie algebras, with families and singleton elements connected by jump deformations.

Contribution

It identifies the stratification pattern of these moduli spaces and describes their decomposition via jump deformations, extending known structures from Lie algebras to superalgebras.

Findings

Moduli spaces are stratified by projective orbifolds.

Presence of families and singleton elements in the moduli spaces.

Stratification linked by jump deformations, consistent with deformation theory.

Abstract

In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of the moduli space by projective orbifolds. The moduli spaces consist of some families as well as some singleton elements. The different strata are linked by jump deformations, which gives a uniques manner of decomposing the moduli space which is consistent with deformation theory.