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 simultaneously adding to it a central element
and an outer derivation so that the larger algebra has also a NIS. Affine loop
algebras, Lie (super)algebras with symmetrizable Cartan matrix over any field,
Manin triples, symplectic reflection (super)algebras are among the Lie
(super)algebras suitable to be doubly extended.
We consider double extensions of Lie superalgebras in characteristic 2, and
concentrate on peculiarities of these notions related with the possibility for
the bilinear form, the center, and the derivation to be odd. Two Lie
superalgebras we discovered by this method are indigenous to the characteristic
2.Comment: To appear in Journal of Algebr
