Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sandwich classification for $O_{2n+1}(R)$ and $U_{2n+1}(R,\Delta)$
  revisited   In a recent paper, the author proved that if $n\geq 3$ is a natural number,
$R$ a commutative ring and $\sigma\in GL_n(R)$, then $t_{kl}(\sigma_{ij})$
where $i\neq j$ and $k\neq l$ can be expressed as a product of $8$ matrices of
the form $^{\epsilon}\sigma^{\pm 1}$ where $\epsilon\in E_n(R)$. In this
article we prove similar results for the odd-dimensional orthogonal groups
$O_{2n+1}(R)$ and the odd-dimensional unitary groups $U_{2n+1}(R,\Delta)$ under
the assumption that $R$ is commutative and $n\geq 3$. This yields new, short
proofs of the Sandwich Classification Theorems for the groups $O_{2n+1}(R)$ and
$U_{2n+1}(R,\Delta)$.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an