# Revista Matemática Iberoamericana

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**Volume 27, Issue 2, 2011, pp. 621–644**

**DOI: 10.4171/RMI/649**

The center of a Leavitt path algebra

Gonzalo Aranda Pino^{[1]}and Kathi Crow

^{[2]}(1) Departamento de Algebra, Geometría y Topología, Universidad de Málaga, 29071, MÁLAGA, SPAIN

(2) Department of Mathematics, Salem State University, MA 01970, SALEM, UNITED STATES

In this paper the center of a Leavitt path algebra is computed for a wide range of situations. A basis as a $K$-vector space is found for $Z(L(E))$ when $L(E)$ enjoys some finiteness condition such as being artinian, semisimple, noetherian and locally noetherian. The main result of the paper states that a simple Leavitt path algebra $L(E)$ is central (i.e. the center reduces to the base field $K$) when $L(E)$ is unital and has zero center otherwise. Finally, this result is extended, under some mild conditions, to the case of exchange Leavitt path algebras.

*Keywords: *Leavitt path algebra, graph algebra, center

Aranda Pino Gonzalo, Crow Kathi: The center of a Leavitt path algebra. *Rev. Mat. Iberoamericana* 27 (2011), 621-644. doi: 10.4171/RMI/649