The center of a Leavitt path algebra

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.