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

TL;DR

This paper establishes unique prime factorization results for certain tensor products of type II_1 factors derived from generalized q-Gaussian algebras, advancing understanding of their structural properties.

Contribution

It provides the first unique prime factorization results for tensor products of generalized q-Gaussian von Neumann algebras with specific conditions on the underlying spaces.

Findings

Proved unique prime factorization for tensor products of these algebras.

Identified conditions on the dimensions of the spaces involved.

Extended the structural theory of q-Gaussian von Neumann algebras.

Abstract

We prove some unique prime factorization results for tensor products of type $II_1$ factors of the form $\Gamma_q(\mathbb{C}, S \otimes H)$ arising from symmetric independent copies with sub-exponential dimensions of the spaces $D_k(S)$ and dim$(H)$ finite and greater than a constant depending on $q$.