Centers of Leavitt path algebras and their completions

TL;DR

This paper provides a new characterization of the center of a Leavitt path algebra, linking it to the Boolean algebra of finitary annihilator hereditary subsets of the underlying finite graph.

Contribution

It introduces a novel approach to describe the center of Leavitt path algebras using Boolean algebra of hereditary subsets, differing from previous graph-based characterizations.

Findings

Boolean algebra of central idempotents is isomorphic to hereditary subsets

New characterization applies to Leavitt path algebras of finite graphs

Enhances understanding of algebraic structure related to graph properties

Abstract

In [8, 9] M. G. Corrales Garcia, D. M. Barquero, C. Martin Gonzalez, M. Siles Molina, J. F 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.