Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Lie Algebras   In this paper, the notion of universal enveloping algebra introduced in [A.
Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected Braided
Bialgebras}, submitted. (arXiv:0805.3391v3)] is specialized to the case of
braided vector spaces whose Nichols algebra is quadratic as an algebra. In this
setting a classification of universal enveloping algebras for braided vector
spaces of dimension not greater than 2 is handled. As an application, we
investigate the structure of primitively generated connected braided bialgebras
whose braided vector space of primitive elements forms a Nichols algebra which
is quadratic algebra.

24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat