Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manin Triples and Non-degenerate Anti-symmetric Bilinear Forms on Lie
  Superalgebras in Characteristic $2$   In this paper, we consider the notions of Manin triples and double extensions
for a Lie superalgebra $\mathfrak{g}$ defined over a field of characteristic
$p=2$. We found cohomological necessary conditions for the pair $(\mathfrak{g},
\mathfrak{g}^*)$ to form a Manin triple. We introduce the concept of
bi-superalgebras for $p=2$ and established a link between Manin triples and
bi-superalgebras. We show that any double extension of any Manin triple is also
a~Manin triple.
  We introduce the notion of left-symmetric structures - also known as Vinberg
structures - on Lie algebras in characteristic $2$ and show that every Lie
algebra with an invertible derivation gives rise to a left-symmetric structure
on it. We then show that every ${\mathbb Z}/2-$graded Lie algebra with an
invertible derivation can be endowed with a Lie superalgebra structure if the
associator of the corresponding left-symmetric structure vanishes. In
particular, if the Lie algebra is 2-step nilpotent, then the associator
vanishes.
  Due to the distinguished role of the squaring on the Lie superalgebra in
characteristic $2$, all these notions require special approaches as compared to
their analogs in other characteristics.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg