Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple, locally finite dimensional Lie algebras in positive
  characteristic   We prove two structure theorems for simple, locally finite dimensional Lie
algebras over an algebraically closed field of characteristic $p$ which give
sufficient conditions for the algebras to be of the form $[R^{(-)}, R^{(-)}] /
(Z(R) \cap [R^{(-)}, R^{(-)}])$ or $[K(R, *), K(R, *)]$ for a simple, locally
finite dimensional associative algebra $R$ with involution $*$. The first
proves that a condition we introduce, known as locally nondegenerate, along
with the existence of an ad-nilpotent element suffice. The second proves that a
uniformly ad-integrable Lie algebra is of this type if the characteristic of
the ground field is sufficiently large. Lastly we construct a simple, locally
finite dimensional associative algebra $R$ with involution $*$ such that $K(R,
*) \ne [K(R, *), K(R, *)]$ to demonstrate the necessity of considering the
commutator in the first two theorems.

17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex