Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

DOI10.1515/CRELLE.2010.023zbMath1207.46049arXiv0809.0164OpenAlexW2164850383MaRDI QIDQ3553934

Aidan Sims, Takeshi Katsura, Paul S. Muhly, Mark Tomforde

Publication date: 22 April 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.0164

zbMATH Keywords

Morita equivalencegraph \(C^*\)-algebrasCuntz-Krieger algebrasExel-Laca algebrasgauge-invariant uniqueness theoremultragraph algebras

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

Related Items (18)

Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras ⋮ Realizing ultragraph Leavitt path algebras as Steinberg algebras ⋮ Characterizing Rickart and Baer ultragraph Leavitt path algebras ⋮ On the ideals of ultragraph Leavitt path algebras ⋮ On ultragraph Leavitt path algebras with finite Gelfand-Kirillov dimension ⋮ A Cuntz-Krieger uniqueness theorem for semigraph \(C^\ast\)-algebras ⋮ -algebras of labelled graphs III—-theory computations ⋮ SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY ⋮ Monopoles, dipoles, and harmonic functions on Bratteli diagrams ⋮ KMS and ground states on ultragraph \( C^*\)-algebras ⋮ Continuous shift commuting maps between ultragraph shift spaces ⋮ Monic representations of the Cuntz algebra and Markov measures ⋮ Representations and the reduction theorem for ultragraph Leavitt path algebras ⋮ 𝑊-Markov measures, transfer operators, wavelets and multiresolutions ⋮ Unique tracial state on the labeled graph C∗-algebra associated to the Thue–Morse sequence ⋮ Purely infinite simple ultragraph Leavitt path algebras ⋮ Irreducible and permutative representations of ultragraph Leavitt path algebras ⋮ Branching systems and general Cuntz–Krieger uniqueness theorem for ultragraph C^*-algebras

Cites Work

• Graphs, groupoids, and Cuntz-Krieger algebras
• Cuntz-Krieger algebras of directed graphs
• A class of C*-algebras and topological Markov chains
• \(C^*\)-algebras of real rank zero
• The \(K\)-theory of Cuntz-Krieger algebras for infinite matrices
• Simplicity of Cuntz-Krieger algebras of infinite matrices.
• Simplicity of ultragraph algebras
• Ultragraph C^*-algebras via topological quivers
• Cuntz-Krieger algebras of infinite graphs and matrices
• The range of K-Invariants for C*-Algebras of infinite graphs
• Real rank of C*-algebras associated with graphs
• The 𝐶*-algebras of infinite graphs

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