Double extensions of quasi-Frobenius Lie superalgebras with degenerate center

TL;DR

This paper extends the theory of symplectic double extensions to Lie superalgebras with degenerate centers, providing standard models and demonstrating their equivalence to orthosymplectic or periplectic types, with illustrative low-dimensional examples.

Contribution

It introduces a superization of symplectic double extensions for Lie superalgebras with degenerate centers, expanding previous work and establishing standard models and equivalence results.

Findings

Standard models for double extensions with orthosymplectic or periplectic forms

Equivalence of all double extensions to these standard types

Examples illustrating the concepts in low dimensions

Abstract

We develop the process of symplectic double extensions for Lie superalgebras with degenerate center. The construction is a superization of a recent work by Fischer, and generalize our previous work. We provide a standard model for such double extensions, where the symplectic form is either orthosymplectic or periplectic. Additionally, we show that every double extension is naturally equivalent to either of these two standard types of extensions. Several examples in low dimensions are given to illustrate the concept.