Double extensions of quasi-Frobenius Lie superalgebras with degenerate center

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.

References in corpus (3)

• Computer-aided study of double extensions of restricted Lie superalgebras preserving the non-degenerate closed 2-forms in characteristic 2
• Extensions of (super) Lie algebras
• Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras