Representation theory and numerical AF-invariants. The representations and centralizers of certain states on 𝒪_{𝒹}

DOI10.1090/memo/0797zbMath1060.46048arXivmath/9907036OpenAlexW4256317371MaRDI QIDQ4458913

Palle E. T. Jorgensen, Ola Bratteli, Vasyl L. Ostrovskyĭ

Publication date: 14 March 2004

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9907036

zbMATH Keywords

KMS states Cuntz algebras dimension groups AF-algebras toral actions numerical AF-invariants

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Dilations, extensions, compressions of linear operators (47A20) Symbolic dynamics (37B10) Representation theory of linear operators (47A67) States of selfadjoint operator algebras (46L30)

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Infinite weighted graphs with bounded resistance metric ⋮ Classification of the direct limits of involution simple associative algebras and the corresponding dimension groups. ⋮ Baumslag-Solitar group \(C^*\)-algebras from interval maps ⋮ Minimal Bratteli diagrams and the dimension groups of AF \(C^{*}\)-algebras ⋮ Atomic representations of Cuntz algebras ⋮ Monopoles, dipoles, and harmonic functions on Bratteli diagrams ⋮ Pure states on Cuntz algebras arising from geometric progressions ⋮ Purely atomic representations of higher-rank graph \(C^*\)-algebras ⋮ Monic representations of the Cuntz algebra and Markov measures ⋮ Cuntz-Krieger algebras representations from orbits of interval maps ⋮ Noncommutative Boundaries Arising in Dynamics and Representations of the Cuntz Relations ⋮ Unbounded representations of \(q\)-deformation of Cuntz algebra ⋮ \(N\)-parameter Fibonacci AF-algebras are isomorphic to their transpose AF-algebras ⋮ Disintegration of projective measures ⋮ Measures in wavelet decompositions ⋮ Classification of sub-Cuntz states ⋮ Orbit representations from matrices

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