Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity

Marius Junge; Bogdan Udrea

Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity

Operator Algebras 2018-09-20 v3

Authors: Marius Junge , Bogdan Udrea

Abstract

We define $\Gamma_q(B,S \otimes H)$ , the generalized $q$ -gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(\pi_j,B,A,D)$ 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 non-isomorphism and non-embedability results about some of these von Neumann algebras.

Keywords

von Neumann algebras q-Gaussian strong solidity non-isomorphism non-embedability operator algebras coefficients

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@article{arxiv.1509.07069,
  title  = {Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity},
  author = {Marius Junge and Bogdan Udrea},
  journal= {arXiv preprint arXiv:1509.07069},
  year   = {2018}
}

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Generalized $q$-Gaussian von Neumann algebras with coefficients, I. Relative strong solidity

Abstract

Keywords

Cite

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