Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cluster variety face of quantum groups   Using the well-known free-field formalism for quantum groups, we demonstrate
in case of $A(n)_q$, that quantum group is naturally also a cluster variety.
Widely used formulae for mutations are direct consequence of independence of
group element on the order of simple roots. Usual formulae for $2 n$ Poisson
leaf emerge in classical limit, if all but few ($2n$) coordinates vanish.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph