Remarks on factoriality and q-deformations

Adam Skalski; Simeng Wang

doi:10.1090/proc/13715

Remarks on factoriality and q-deformations

Adam Skalski
, Simeng Wang

Institute of Mathematics of the Polish Academy of Sciences
CNRS
Saarland University

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We prove that the mixed q-Gaussian algebra Γ_Q (H_ℝ) associated to a real Hilbert space H ℝ and a real symmetric matrix Q = (qij) with sup |qij| < 1, is a factor as soon as dim H_ℝ ≥ 2. We also discuss the factoriality of q-deformed Araki-Woods algebras, in particular showing that the q-deformed Araki-Woods algebra Γ_q(H_ℝ, U_t) given by a real Hilbert space H_ℝ and a strongly continuous group U_t is a factor when dim H_ℝ ≥ 2 and U_t admits an invariant eigenvector.

Original language	English
Pages (from-to)	3813-3823
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	9
DOIs	https://doi.org/10.1090/proc/13715
State	Published - 2018
Externally published	Yes

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title = "Remarks on factoriality and q-deformations",

abstract = "We prove that the mixed q-Gaussian algebra ΓQ (Hℝ) associated to a real Hilbert space H ℝ and a real symmetric matrix Q = (qij) with sup |qij| < 1, is a factor as soon as dim Hℝ ≥ 2. We also discuss the factoriality of q-deformed Araki-Woods algebras, in particular showing that the q-deformed Araki-Woods algebra Γq(Hℝ, Ut) given by a real Hilbert space Hℝ and a strongly continuous group Ut is a factor when dim Hℝ ≥ 2 and Ut admits an invariant eigenvector.",

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AB - We prove that the mixed q-Gaussian algebra ΓQ (Hℝ) associated to a real Hilbert space H ℝ and a real symmetric matrix Q = (qij) with sup |qij| < 1, is a factor as soon as dim Hℝ ≥ 2. We also discuss the factoriality of q-deformed Araki-Woods algebras, in particular showing that the q-deformed Araki-Woods algebra Γq(Hℝ, Ut) given by a real Hilbert space Hℝ and a strongly continuous group Ut is a factor when dim Hℝ ≥ 2 and Ut admits an invariant eigenvector.

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Remarks on factoriality and q-deformations

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