Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Involutions of sl(2,k) and non-split, three-dimensional simple Lie
  algebras   We give a process to construct non-split, three-dimensional simple Lie
algebras from involutions of sl(2,k), where k is a field of characteristic not
two. Up to equivalence, non-split three-dimensional simple Lie algebras
obtained in this way are parametrised by a subgroup of the Brauer group of k
and are characterised by the fact that their Killing form represents -2. Over
local and global fields we re-express this condition in terms of Hilbert and
Legendre Symbols and give examples of three-dimensional simple Lie algebras
which can and cannot be obtained by this construction over the field of
rationals.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics