The main purpose of this paper is to study restricted formal deformations of restricted Lie-
Rinehart algebras in positive characteristic $ p $. For $ p> 2$, we discuss the deformation …

We review the list of non-degenerate invariant (super) symmetric bilinear forms (briefly: NIS)
on the following simple (relatives of) Lie (super) algebras:(a) with symmetrizable Cartan …

All results concern characteristic 2. We describe two procedures; each of which to every
simple Lie algebra assigns a simple Lie superalgebra. We prove that every simple finite …

In this paper, we present a method of symplectic double extensions for restricted quasi-
Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent …

A Lie (super) algebra with a nondegenerate invariant symmetric bilinear form B is called a
nis-(super) algebra. The double extension g of a nis-(super) algebra a is the result of …

In this paper, we introduce and develop the notion of a Manin triple for a Lie superalgebra g
defined over a field of characteristic p= 2. We find cohomological necessary conditions for …

The main goal of this paper was to develop the structure theory of Hom-Lie superalgebras in
characteristic 2. We discuss their representations, semidirect product, and α k-derivations …

A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-
degenerate bilinear form. We study the notion of double extensions of quasi-Frobenius Lie …

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 …

As is well-known, the dimension of the space spanned by the non-degenerate invariant
symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie …