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

2015/09/23 by Junge, Marius, Udrea, Bogdan
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1509.07069

Abstract

We define Γ_q(B,S ⊗ 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 ∈ 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 non-isomorphism and non-embedability results about some of these von Neumann algebras.

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