Vol. 12, No. 7, 2019

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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
Abstract

We define Γq(B,S H), the generalized q-gaussian von Neumann algebras associated to a sequence of symmetric independent copies (πj,B,A,D) and to a subset 1 S = S 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