Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric realization of Khovanov-Lauda-Rouquier algebras associated
  with Borcherds-Cartan data   We construct a geometric realization of the Khovanov-Lauda-Rouquier algebra
$R$ associated with a symmetric Borcherds-Cartan matrix $A=(a_{ij})_{i,j\in I}$
via quiver varieties. As an application, if $a_{ii} \ne 0$ for any $i\in I$, we
prove that there exists a 1-1 correspondence between Kashiwara's lower global
basis (or Lusztig's canonical basis) of $U_\A^-(\g)$ (resp.\ $V_\A(\lambda)$)
and the set of isomorphism classes of indecomposable projective graded modules
over $R$ (resp.\ $R^\lambda$).

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int