Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and
  PostLie algebras   We generalize the classical study of (generalized) Lax pairs and the related
$O$-operators and the (modified) classical Yang-Baxter equation by introducing
the concepts of nonabelian generalized Lax pairs, extended $\calo$-operators
and the extended classical Yang-Baxter equation. We study in this context the
nonabelian generalized $r$-matrix ansatz and the related double Lie algebra
structures. Relationship between extended $O$-operators and the extended
classical Yang-Baxter equation is established, especially for self-dual Lie
algebras. This relationship allows us to obtain explicit description of the
Manin triples for a new class of Lie bialgebras. Furthermore, we show that a
natural structure of PostLie algebra is behind $O$-operators and fits in a
setup of triple Lie algebra that produces self-dual nonabelian generalized Lax
pairs.

29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con