Factoriality of \(q\)-Gaussian von Neumann algebras

DOI10.1007/S00220-004-1266-5zbMath1079.81038arXivmath/0311413OpenAlexW1968124414MaRDI QIDQ2571142

Éric Ricard

Publication date: 1 November 2005

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

Full work available at URL: https://arxiv.org/abs/math/0311413

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) General theory of von Neumann algebras (46L10)

Related Items (36)

Hypercontractivity in non-commutative holomorphic spaces ⋮ Asymptotic matricial models and QWEP property for \(q\)-Araki-Woods algebras ⋮ A simple proof of the complete metric approximation property for $q$-Gaussian algebras ⋮ On the isomorphism class of 𝑞-Gaussian C*-algebras for infinite variables ⋮ The radial MASA in free orthogonal quantum groups ⋮ On the commutants of generators of \(q\)-deformed Araki-Woods von Neumann algebras ⋮ Remarks on factoriality and 𝑞-deformations ⋮ Mixed \(q\)-deformed Araki-Woods von Neumann algebras ⋮ $q$-Araki-Woods algebras: Extension of second quantisation and Haagerup approximation property ⋮ Quantum groups, non-commutative \(AdS_2\), and chords in the double-scaled SYK model ⋮ Conjugate variables approach to mixed q-Araki–Woods algebras: Factoriality and non-injectivity ⋮ A dual and conjugate system for \(q\)-Gaussians for all \(q\) ⋮ Fock representations of Q-deformed commutation relations ⋮ Full solution of the factoriality question for \(q\)-Araki-Woods von Neumann algebras via conjugate variables ⋮ \(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ Modular structure and inclusions of twisted Araki-Woods algebras ⋮ The bulk Hilbert space of double scaled SYK ⋮ On the factoriality of \(q\)-deformed Araki-Woods von Neumann algebras ⋮ Noncommutative probability of type D ⋮ Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations ⋮ Exactness of the Fock space representation of the \(q\)-commutation relations ⋮ Free monotone transport ⋮ BESSIS–MOUSSA–VILLANI CONJECTURE AND GENERALIZED GAUSSIAN RANDOM VARIABLES ⋮ The \((q, t)\)-Gaussian process ⋮ The von Neumann algebras generated by \(t\)-Gaussians ⋮ Fock space associated to Coxeter groups of type B ⋮ An application of free transport to mixed 𝑞-Gaussian algebras ⋮ On MASAs in \(q\)-deformed von Neumann algebras ⋮ Singularity of the generator subalgebra in mixed $q$-Gaussian algebras ⋮ Generalized \(q\)-Gaussian von Neumann algebras with coefficients. I. Relative strong solidity ⋮ Noncommutative maximal ergodic theorems ⋮ On the von Neumann algebras associated to Yang–Baxter operators ⋮ Connes' bicentralizer problem for q‐deformed Araki–Woods algebras ⋮ Contractivity properties of Ornstein–Uhlenbeck semigroup for mixed q-Araki–Woods von Neumann algebras ⋮ Singularity of the generator subalgebra in 𝑞-Gaussian algebras ⋮ Generator masas in \(q\)-deformed Araki-Woods von Neumann algebras and factoriality

Cites Work

• Factoriality of Bożejko-Speicher von Neumann algebras
• An example of a generalized Brownian motion
• Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces
• \(q\)-Gaussian processes: Non-commutative and classical aspects
• Non-injectivity of the \(q\)-deformed von Neumann algebra

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