#### 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 ${\Gamma }_{q}\left(B,S\otimes H\right)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $\left({\pi }_{j},B,A,D\right)$ and to a subset $1\in S={S}^{\ast }\subset A$ 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.

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