Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras

Sofiane Bouarroudj   ; Quentin Ehret   ; Yoshiaki Maeda

Symmetry, integrability and geometry: methods and applications, Tome 19 (2023)

Résumé

In this paper, we present a method of symplectic double extensions for restricted quasi-Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent obstructions to symplectic double extension, which we fully describe. We found a necessary condition for which a restricted quasi-Frobenius Lie superalgebras is a symplectic double extension of a smaller restricted Lie superalgebra. The constructions are illustrated with a few examples.

Détail

Keywords: restricted Lie (super)algebra, quasi-Frobenius Lie (super)algebra, double extension.

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