$q$-Araki-Woods algebras: Extension of second quantisation and Haagerup approximation property

DOI10.1090/proc/13681zbMath1385.46043arXiv1605.06034OpenAlexW2963460489MaRDI QIDQ4592753

Mateusz Wasilewski

Publication date: 8 November 2017

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

Full work available at URL: https://arxiv.org/abs/1605.06034

zbMATH Keywords

Haagerup approximation propertysecond quantisation\(q\)-Araki-Woods algebra

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10)

Related Items (7)

A simple proof of the complete metric approximation property for $q$-Gaussian algebras ⋮ Remarks on factoriality and 𝑞-deformations ⋮ Complete metric approximation property for \(q\)-Araki-Woods algebras ⋮ Poisson boundary on full Fock space ⋮ Mixed \(q\)-deformed Araki-Woods von Neumann algebras ⋮ On the factoriality of \(q\)-deformed Araki-Woods von Neumann algebras ⋮ Optimal speed of response in the Lotka-Volterra controlled system

Cites Work

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• Free quasi-free states
• Non-injectivity of the \(q\)-deformed von Neumann algebra
• Generator masas in \(q\)-deformed Araki-Woods von Neumann algebras and factoriality
• Factoriality of \(q\)-Gaussian von Neumann algebras
• The Haagerup property for locally compact quantum groups
• The Haagerup Property for Arbitrary von Neumann Algebras
• Locally compact quantum groups in the von Neumann algebraic setting
• Remarks on factoriality and 𝑞-deformations

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