Non injectivity of the q-deformed von Neumann algebra
type: Dataset
description: We prove that the von Neumann algebra generated by q-gaussians is not injective as soon as the dimension of the underlying Hilbert space is greater than 1. Our approach is based on a vector valued Khintchine type inequality for Wick products. The same proof also works for the more general setting of a Yang-Baxter deformation. Our techniques can also be extended to the so called q-Araki-Woods von Neumann algebras recently introduced by Hiai. In this latter case, we obtain the non injectivity under some asssumption on the spectral set of the positive operator associated with the deformation.
landing page: 0025-5831
keyword: 46l65-46l54
keyword: deformation
keyword: gaussian
keyword: infoeu-reposemanticsarticle
keyword: injectivity
keyword: journal-articles
keyword: mathmath-oamathematics-mathoperator-algebras-mathoa
keyword: yang-baxter-operator
issued: 2026-05-15T07:30:04.080985
modified: 2026-05-15T07:30:04.080992
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Non injectivity of the q-deformed von Neumann algebra
type: Distribution
format: HTML
access URL: https://hal.science/hal-00077597
issued: 2026-05-15T07:30:04.109327
modified: 2026-05-15T07:30:04.065031