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 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 …

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 …

Over $\mathbb {C} $, Montgomery superized Herstein's construction of simple Lie algebras
from finite-dimensional associative algebras, found obstructions to the procedure and …

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 …

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 …

Using tensor categories, we present new constructions of several of the exceptional simple
Lie superalgebras with integer Cartan matrix in characteristic p= 3 and p= 5 from the …

Over algebraically closed fields of positive characteristic, for simple Lie (super) algebras,
and certain Lie (super) algebras close to simple ones, with symmetric root systems (such …