Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded simple Lie algebras and graded simple representations   For any finitely generated abelian group $Q$, we reduce the problem of
classification of $Q$-graded simple Lie algebras over an algebraically closed
field of "good" characteristic to the problem of classification of gradings on
simple Lie algebras. In particular, we obtain the full classification of
finite-dimensional $Q$-graded simple Lie algebras over any algebraically closed
field of characteristic $0$ based on the recent classification of gradings on
finite dimensional simple Lie algebras.
  We also reduce classification of simple graded modules over any $Q$-graded
Lie algebra (not necessarily simple) to classification of gradings on simple
modules. For finite-dimensional $Q$-graded semisimple algebras we obtain a
graded analogue of the Weyl Theorem.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom