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 …

1) In 1976, looking at simple finite-dimensional complex Lie superalgebras, J.~ Bernstein
and I, and independently M.~ Duflo, observed that certain divergence-free vectorial Lie …

A Lie (super) algebra with a non-degenerate invariant symmetric bilinear form will be called
a NIS-Lie (super) algebra. The double extension of a NIS-Lie (super) algebra is the result of …

We overview the classifications of simple finite-dimensional modular Lie algebras. In
characteristic 2, their list is wider than that in other characteristics; eg, it contains …

Lately, the following were observed:(1) an upsurge of interest (in particular, triggered by a
paper by Atiyah and Witten) to manifolds with G (2)-type structure;(2) classifications are …

Abstract A double extension (D D-extension) of a Lie (super) algebra aa with a non-
degenerate invariant symmetric bilinear form BB, briefly, a NIS-(super) algebra, is an …

It is demonstrated how a simple linear-algebraic technique used earlier to compute the low-
degree cohomology of current Lie algebras, can be utilized to compute other kinds of …

The ground field in the text is of characteristic 2. The classification of modulo 2 gradings of
simple Lie algebras is vital for the classification of simple finite-dimensional Lie …