C*-equivalences of graphs

1998/10/15 by D. Drinen, Drinen, D., Nándor Sieben +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/9810100

16 pages, AMSLaTeX, XY-pic, minor changes (including new definition of primitive transfer to avoid pathological cases)

openalex publication_date 1998/10/15 · arxiv created 1999/02/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.

Citations

• A class ofC *-algebras and topological Markov chains

Related

• Strong Shift Equivalence in the C*-algebraic setting: Graphs and C*-correspondences
• Renault's Equivalence Theorem for Reduced Groupoid C*-algebras
• Refined moves for structure-preserving isomorphism of graph C*-algebras
• Correspondences between graph C*-algebras
• Moves on k-graphs preserving Morita equivalence