Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization problem with intersection   We propose a generalization of the factorization method to the case when
$\mathcal{G}$ is a finite dimensional Lie algebra such that
$\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces),
where $\mathcal{G}_0$ is a subalgebra in $\mathcal{G}$, $M, N$ are
$\mathcal{G}_0$-modules, and $\mathcal{G}_0 +M$, $\mathcal{G}_0 +N$ are
subalgebras in $\mathcal{G}$. In particular, we consider the case when
$\mathcal{G}$ is a $\Z$-graded Lie algebra. Using this generalization, we
construct some top-like systems related to the algebra $so(3,1)$. According to
the general scheme, these systems can be reduced to linear systems with
variable coefficients. For the top-like systems first integrals and
infinitesimal symmetries are found.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin