Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An abstract characterization of noncommutative projective lines   Let $k$ be a field. We describe necessary and sufficient conditions for a
$k$-linear abelian category to be a noncommutative projective line, i.e. a
noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$.
As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th
noncommutative projective line, is the noncommutative projectivization of an
$n$-dimensional vector space.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th