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The Leavitt path algebra of a graph

G. Abrams·G. Aranda Pino
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Abstract

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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G. Abrams, G. Aranda Pino. 2005-09-21. The Leavitt path algebra of a graph. https://arxiv.org/abs/math/0509494

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