A \(C^*\)-Algebra Construction for Undirected Graphs

  • Erin Brownlee
  • Benton L. DuncanEmail author


To each undirected graph, we associate an edge-colored directed graph and hence a universal and reduced \(C^*\)-algebra. We then use results on edge-colored directed graphs to completely describe the universal and reduced undirected graph \(C^*\)-algebras in the case of finite graphs. We extend the descriptions of the universal algebra to arbitrary undirected graphs using direct limits.


Undirected graph Edge-colored directed graph Separated graph \(C^*\)-algebra 

Mathematics Subject Classification

46L05 46L09 



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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorthern State UniversityAberdeenUSA
  2. 2.Department of MathematicsNorth Dakota State UniversityFargoUSA

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