Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric Lie algebras and quadratic extensions   The present paper contains a systematic study of the structure of metric Lie
algebras, i.e., finite-dimensional real Lie algebras equipped with a
non-degenerate invariant symmetric bilinear form. We show that any metric Lie
algebra without simple ideals has the structure of a so called balanced
quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module A
in a canonical way. Identifying equivalence classes of quadratic extensions of
l by A with a certain cohomology set H^2_Q(l,A) we obtain a classification
scheme for general metric Lie algebras and a complete classification of metric
Lie algebras of index 3.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio