Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple Lie Color Algebras of Weyl Type   For an $(\epsilon,G)$-color-commutative associative algebra $A$ with an
identity element over a field $F$ of characteristic not 2, and for a
color-commutative subalgebra $D$ of color-derivations of $A$, denote by $A[D]$
the associative subalgebra of ${\rm End}(A)$ generated by $A$ (regarding as
operators on $A$ via left multiplication) and $D$. It is easily proved that, as
an associative algebra, $A[D]$ is $G$-graded simple if and only if $A$ is
$\G$-graded $D$-simple. Suppose $A$ is $\G$-graded $D$-simple. Then,
  (a) $A[D]$ is a free left $A$-module;
  (b) as a Lie color algebra, the subquotient
$[A[D],A[D]]/Z(A[D])\cap[A[D],A[D]]$ is simple (except one minor case), where
$Z(A[D])$ is the color center of $A[D]$.
  The structure of this subquotient is explicitly described.

0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio