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Using the Steinberg algebra model to determine the center of any Leavitt path algebra

  • Lisa Orloff Clark
  • Dolores Martín Barquero
  • Cándido Martín González
  • Mercedes Siles Molina
Article

Abstract

Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open invariant subsets of the unit space of the graph groupoid in terms of the underlying graph: an open invariant subset is compact if and only if its associated hereditary and saturated set of vertices satisfies Condition (F). We also give a basis of the center. Its cardinality depends on the number of minimal compact open invariant subsets of the unit space.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Lisa Orloff Clark
    • 1
  • Dolores Martín Barquero
    • 2
  • Cándido Martín González
    • 3
  • Mercedes Siles Molina
    • 3
  1. 1.School of Mathematics and StatisticsVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Departamento de Matemática Aplicada, Escuela de Ingenierías IndustrialesUniversidad de MálagaMálagaSpain
  3. 3.Departamento de Álgebra Geometría y Topología, Facultad de CienciasUniversidad de MálagaMálagaSpain

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