Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie Groups, Cluster Variables and Integrable Systems   We discuss the Poisson structures on Lie groups and propose an explicit
construction of the integrable models on their appropriate Poisson
submanifolds. The integrals of motion for the SL(N)-series are computed in
cluster variables via the Lax map. This construction, when generalised to the
co-extended loop groups, gives rise not only to several alternative
descriptions of relativistic Toda systems, but allows to formulate in general
terms some new class of integrable models.

28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics