Viewing AF-algebras as graph algebras

1998/04/21 by D. Drinen, Drinen, D.
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/9804101

11 pages LaTeX. Uses pb-diagram.sty

arxiv created 1998/04/21 · openalex publication_date 1998/04/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Every AF-algebra arises as a graph algebra in the sense of Kumjian, Pask, Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by Stratila and Voiculescu is consistent with Kumjian's notion of diagonal, and the groupoid arising from a well-chosen Bratteli diagram for A coincides with Kumjian's twist groupoid constructed from a diagonal of A.

Related

• Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras
• Every AF-algebra is Morita equivalent to a graph algebra
• Identifying AF-algebras that are graph C*-algebras
• Equivalence of definitions of AF groupoid
• Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras