Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of simple modules over Leavitt path algebras   Let $E$ be a directed graph, $K$ any field, and let $L_K(E)$ denote the
Leavitt path algebra of $E$ with coefficients in $K$. For each rational
infinite path $c^\infty$ of $E$ we explicitly construct a projective resolution
of the corresponding Chen simple left $L_K(E)$-module $V_{[c^\infty]}$.
Further, when $E$ is row-finite, for each irrational infinite path $p$ of $E$
we explicitly construct a projective resolution of the corresponding Chen
simple left $L_K(E)$-module $V_{[p]}$. For Chen simple modules $S,T$ we
describe ${\rm Ext}_{L_K(E)}^1(S,T)$ by presenting an explicit $K$-basis. For
any graph $E$ containing at least one cycle, this description guarantees the
existence of indecomposable left $L_K(E)$-modules of any prescribed finite
length.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio