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

TL;DR

This paper proves that certain generalized $q$-Gaussian von Neumann algebras with coefficients lack non-trivial central sequences, highlighting their structural rigidity under specific conditions.

Contribution

It establishes the absence of non-trivial central sequences in a broad class of generalized $q$-Gaussian von Neumann algebras with coefficients, extending previous results.

Findings

No non-trivial central sequences in the specified algebras

Structural rigidity of these von Neumann algebras

Conditions on dimensions ensuring the result

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.