Spectral truncations in noncommutative geometry and operator systems

DOI10.1007/s00220-020-03825-xzbMath1475.46062arXiv2004.14115OpenAlexW3022334257MaRDI QIDQ2021635

Alain Connes, Walter D. van Suijlekom

Publication date: 27 April 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.14115

zbMATH Keywords

spectral truncationoperator systems$C^*$-envelope

Mathematics Subject Classification ID

Noncommutative topology (46L85) Operator spaces and completely bounded maps (46L07) Noncommutative function spaces (46L52) States of selfadjoint operator algebras (46L30)

Related Items (21)

C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems ⋮ Toeplitz separability, entanglement, and complete positivity using operator system duality ⋮ Tolerance relations and operator systems ⋮ Polynomial approximation of quantum Lipschitz functions ⋮ The Podleś spheres converge to the sphere ⋮ On multimatrix models motivated by random noncommutative geometry. II: A Yang-Mills-Higgs matrix model ⋮ Tolerance relations and quantization ⋮ Modular spectral triples and deformed Fredholm modules ⋮ The gauge group and perturbation semigroup of an operator system ⋮ Characterizations of ordered self-adjoint operator spaces ⋮ A comparison of two quantum distances ⋮ Convergence of Fourier truncations for compact quantum groups and finitely generated groups ⋮ Convergence of inductive sequences of spectral triples for the spectral propinquity ⋮ Gromov-Hausdorff convergence of spectral truncations for tori ⋮ Operator systems for tolerance relations on finite sets ⋮ On multimatrix models motivated by random noncommutative geometry. I: The functional renormalization group as a flow in the free algebra ⋮ Weil positivity and trace formula the Archimedean place ⋮ Dual spaces of operator systems ⋮ The operator system of Toeplitz matrices ⋮ Truncated geometry on the circle ⋮ Phase transition in random noncommutative geometries

Uses Software

• Vandermonde Tools

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