The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules

DOI10.1142/S1793525317500108zbMath1370.19004arXiv1501.05363OpenAlexW2963029938MaRDI QIDQ2979667

Adam Rennie, David Robertson, Aidan Sims

Publication date: 26 April 2017

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05363

zbMATH Keywords

conditional expectationextensionCuntz-Pimsner algebraKMS stateKasparov moduleToeplitz extension

Mathematics Subject Classification ID

(C^*)-modules (46L08) Kasparov theory ((KK)-theory) (19K35) States of selfadjoint operator algebras (46L30)

Related Items (15)

Non-commutative vector bundles for non-unital algebras ⋮ Crossed product extensions of spectral triples ⋮ Unnamed Item ⋮ Index theory and topological phases of aperiodic lattices ⋮ Constructing KMS states from infinite-dimensional spectral triples ⋮ Poincaré duality for Cuntz-Pimsner algebras ⋮ The bulk-edge correspondence for the quantum Hall effect in Kasparov theory ⋮ Shift–tail equivalence and an unbounded representative of the Cuntz–Pimsner extension ⋮ Gauge theory on noncommutative Riemannian principal bundles ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ Untwisting twisted spectral triples ⋮ A non-commutative framework for topological insulators ⋮ The Cuntz-Pimsner extension and mapping cone exact sequences ⋮ Boundaries, spectral triples and \(K\)-homology ⋮ Real spectral triples on crossed products

Cites Work

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• Pimsner algebras and Gysin sequences from principal circle actions
• Riemannian manifolds in noncommutative geometry
• The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
• Graphs, groupoids, and Cuntz-Krieger algebras
• The noncommutative geometry of graph \(C^*\)-algebras. I: The index theorem
• On certain Cuntz-Pimsner algebras
• Quantum spheres and projective spaces as graph algebras
• KMS states of quasi-free dynamics on Pimsner algebras
• Jones index theory for Hilbert \(C^*\)-bimodules and its equivalence with conjugation theory
• Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
• Functoriality of Cuntz-Pimsner correspondence maps
• Cuntz-Pimsner \(C^*\)-algebras and crossed products by Hilbert \(C^*\)-bimodules
• Equilibrium states on the Cuntz-Pimsner algebras of self-similar actions
• EXACTNESS OF CUNTZ–PIMSNER C^*-ALGEBRAS
• Ergodic actions and spectral triples
• Groupoid cocycles and K-theory
• Twisted cyclic theory, equivariant KK-theory and KMS states
• Algebraic Cuntz-Pimsner rings
• Exel's crossed product and relative Cuntz–Pimsner algebras
• A new look at the crossed product of aC^*-algebra by a semigroup of endomorphisms
• On the nuclearity of certain Cuntz-Pimsner algebras
• On the Simplicity of some Cuntz-Pimsner Algebras
• Representations of Cuntz-Pimsner algebras
• A class of \boldmath{$C^*$}-algebras generalizing both graph algebras and homeomorphism \boldmath{$C^*$}-algebras I, fundamental results
• The 𝐶*-algebras of infinite graphs
• CUNTZ–PIMSNER C*-ALGEBRAS ASSOCIATED WITH SUBSHIFTS
• Dilations of \(C^*\)-correspondences and the simplicity of Cuntz-Pimsner algebras

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