Generalized $q$-Gaussian von Neumann algebras with coefficients, II. Absence of central sequences

Abstract

We show that the generalized $q$-gaussian von Neumann algebras with coefficients ${\Gamma }_q(B,S\otimes H)$ with $B$ a finite dimensional factor, dim$(D_k(S))$ sub-exponential and the dimension of $H$ finite and larger than a constant depending on $q$, have no non-trivial central sequences.

Second version, minor corrections

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• Generalized $q$-Gaussian von Neumann algebras with coefficients, III. Unique prime factorization results