Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of infinite-dimensional Lie algebras, exotic cohomology,
  and integrable nonlinear partial differential equations   The important unsolved problem in theory of integrable systems is to find
conditions guaranteeing existence of a Lax representation for a given PDE. The
use of the exotic cohomology of the symmetry algebras opens a way to formulate
such conditions in internal terms of the PDEs under the study. In this paper we
consider certain examples of infinite-dimensional Lie algebras with nontrivial
second exotic cohomology groups and show that the Maurer-Cartan forms of the
associated extensions of these Lie algebras generate Lax representations for
integrable systems, both known and new ones.

26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci