Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson Yang-Baxter equations and $\mathcal{O}$-operators of Poisson
  superalgebras   We investigate connections between $\mathcal {O}$-operators of Poisson
superalgebras and skew-symmetric solutions of the Poisson Yang-Baxter equation
(PYBE). We prove that a skew-symmetric solution of the PYBE on a Poisson
superalgebra can be interpreted as an $\mathcal {O}$-operator associated to the
co-regular representation. We show that this connection can be enhanced with
symplectic forms when considering non-degenerate skew-symmetric solutions. We
also show that $\mathcal {O}$-operators associated to a general representation
could give skew-symmetric solutions of the PYBE in certain semi-direct product
of Poisson superalgebras.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio