Branching systems and general Cuntz–Krieger uniqueness theorem for ultragraph C*-algebras

DOI10.1142/S0129167X1650083XzbMath1368.46043arXiv1601.07005OpenAlexW2963368431MaRDI QIDQ2831249

Hui Li, Daniel Gonçalves, Danilo Royer

Publication date: 2 November 2016

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.07005

zbMATH Keywords

Perron-Frobenius operatorfaithful representationbranching systemultragraphpermutative representationgeneral Cuntz-Krieger uniqueness theoremultragraph Calgebra

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (11)

Topological freeness for \(C^{\ast}\)-correspondences ⋮ BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS ⋮ Representations of \(C^*\)-algebras of row-countable graphs and unitary equivalence ⋮ SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY ⋮ KMS and ground states on ultragraph \( C^*\)-algebras ⋮ Continuous shift commuting maps between ultragraph shift spaces ⋮ Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems ⋮ Representations and the reduction theorem for ultragraph Leavitt path algebras ⋮ Representations of relative Cohn path algebras ⋮ Irreducible and permutative representations of ultragraph Leavitt path algebras ⋮ Unifying interval maps and branching systems with applications to relative graph \(\mathrm{C}^\ast\)-algebras

Cites Work

• Graph \(C^\ast\)-algebras, branching systems and the Perron-Frobenius operator
• Polynomial endomorphisms of the Cuntz algebras arising from permutations. I: General theory
• A generalized Cuntz-Krieger uniqueness theorem for higher-rank graphs
• Perron-Frobenius operators and representations of the Cuntz-Krieger algebras for infinite matrices
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
• GENERAL CUNTZ–KRIEGER UNIQUENESS THEOREM
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