Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of enveloping algebras of simple Lie algebras and their
  related polynomial algebras   The decomposition problem of the enveloping algebra of a simple Lie algebra
is reconsidered combining both the analytical and the algebraic approach,
showing its relation with the internal labelling problem with respect to a
nilpotent subalgebra. A lower bound for the number of generators of the
commutant as well as the maximal Abelian subalgebra are obtained. The
decomposition problem for the exceptional Lie algebra $G_2$ is completely
solved.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
16
The categories of this paper are: stat