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

2022/10/20 by Caspers, Martijn
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2210.11128

Abstract

Let M_q(H_ℝ) be the q-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space H_ℝ where -1 < q < 1. We show that M_q(H_ℝ) \not ≃ M₀(H_ℝ) for -1 < q \not = 0 < 1. The C^∗-algebraic counterpart of this result was obtained recently in [BCKW22]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras.

Related

• On the isomorphism class of q-Gaussian C^∗-algebras for infinite variables
• Free monotone transport for infinite variables
• Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras
• The von Neumann algebra generated by t-gaussians
• Factoriality of q-Gaussian von Neumann algebras