Centers of Leavitt path algebras and their completions

Abstract

In [9,10] Corrales Garcia, Barquero, Martin Gonzalez, Siles Molina, Solanilla Hernandez described the center of a Leavitt path algebra and characterized it in terms of the underlying graph. We offer a different characterization of the center. In particular, we prove that the Boolean algebra of central idempotents of a Leavitt path algebra of a finite graph is isomorphic to the Boolean algebra of finitary annihilator hereditary subsets of the graph.