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 …

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 …

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 …

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 …

Classification of simple algebras in the Deligne category Rep(St) - ScienceDirect Skip to main
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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 …

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 …

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 …