In this paper the center of a Leavitt path algebra is computed for a wide range of situations. A basis as a -vector space is found for when 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 is central (i.e. the center reduces to the base field ) when is unital and has zero center otherwise. Finally, this result is extended, under some mild conditions, to the case of exchange Leavitt path algebras.
Cite this article
Gonzalo Aranda Pino, Kathi Crow, The center of a Leavitt path algebra. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 621–644DOI 10.4171/RMI/649