Generalized q-gaussian von Neumann algebras with coefficients, I : Relative strong solidity

Junge, Marius; Udrea, Bogdan

doi:10.2140/apde.2019.12.1643

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Generalized $q$-gaussian von Neumann algebras with coefficients, I: Relative strong solidity

Marius Junge and Bogdan Udrea

Vol. 12 (2019), No. 7, 1643–1709

DOI: 10.2140/apde.2019.12.1643

Abstract

We define $Γ_{q} (B, S \otimes H)$ , the generalized $q$ -gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(π_{j}, B, A, D)$ and to a subset $1 \in S = S^{*} \subset A$ and, under certain assumptions, prove their strong solidity relative to $B$ . We provide many examples of strongly solid generalized $q$ -gaussian von Neumann algebras. We also obtain nonisomorphism and nonembedability results about some of these von Neumann algebras.

Keywords

von Neumann algebras, q-gaussian von Neumann algebras with coefficients, relative strong solidity

Mathematical Subject Classification 2010

Primary: 46L10

Milestones

Received: 10 October 2017

Revised: 20 July 2018

Accepted: 16 September 2018

Published: 22 July 2019

Authors

Marius Junge
Department of Mathematics University of Illinois Urbana, IL United States

Bogdan Udrea
Institute of Mathematics of the Romanian Academy Bucharest Romania

Vol. 12, No. 7, 2019