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Centers of Leavitt path algebras and their completions

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arxiv 1507.07439 v2 pith:VRE2HG7J submitted 2015-07-27 math.RA

Centers of Leavitt path algebras and their completions

classification math.RA
keywords algebragraphleavittpathbooleancenteralgebrasannihilator
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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.

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  1. Residual finite-dimensionality of ultragraph algebras via branching systems

    math.OA 2026-07 unverdicted novelty 6.0

    Graph-theoretic RFD conditions on ultragraphs imply RFD for their Leavitt path algebras and C*-algebras, with equivalences under RFUM2 via branching systems and groupoid models.