Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Leavitt path algebra of a graph   For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt
path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of
complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger
algebra $C^*(E)$ described in [8]. The matrix rings $M_n(K)$ and the Leavitt
algebras L(1,n) appear as algebras of the form $L(E)$ for various graphs $E$.
In our main result, we give necessary and sufficient conditions on $E$ which
imply that $L(E)$ is simple.

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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph