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

Abstract

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.

References in corpus (3)

• Restricted simple Lie (super)algebras in characteristic $3$
• Cohomology of Restricted Filiform Lie Algebras ${\mathfrak{m}}_2^{\lambda }(p)$
• Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_{+}(A_1^{(1)})(p)$

Cited by in corpus (1)

• Double extensions of quasi-Frobenius Lie superalgebras with degenerate center