On the isomorphism class of q-Gaussian W-algebras for infinite variables

Martijn Caspers*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Let Mq(HR) be the q-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space HR where −1 < q < 1. We show that Mq(HR) ≠ M0(HR) for −1 < q ≠ 0 < 1. The C-algebraic counterpart of this result was obtained recently in [1]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras.

Original languageEnglish
Pages (from-to)1711-1716
Number of pages6
JournalComptes Rendus Mathematique
Volume361
Issue numberG11
DOIs
Publication statusPublished - 2023

Keywords

  • Akemann–Ostrand property
  • q-Gaussian von Neumann algebras

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