On Degenerations of Lie Superalgebras
Mar\'ia Alejandra Alvarez, Isabel Hern\'andez

TL;DR
This paper investigates the conditions under which one complex Lie superalgebra can degenerate into another, classifies all (2,2)-dimensional cases, and identifies rigid superalgebras including a nilpotent example.
Contribution
It provides necessary conditions for degenerations, a classification of (2,2)-dimensional Lie superalgebras, and discovers a nilpotent rigid superalgebra, expanding understanding of superalgebra structures.
Findings
The variety of (2,2)-dimensional Lie superalgebras has seven irreducible components.
Three components are closures of rigid superalgebras.
An example of a nilpotent rigid Lie superalgebra is found.
Abstract
We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension . As an application, we study the variety of complex Lie superalgebras of dimension . First we give the algebraic classification and then obtain that is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
