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

Abstract

We prove some unique prime factorization results for tensor products of type $I{I}_1$ 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 $q$.

5 pages. This is the first version. Any comments or suggestions are welcome!

References in corpus (2)

• Some prime factorization results for type II_1 factors
• Generalized $q$-Gaussian von Neumann algebras with coefficients, II. Absence of central sequences

Cited by in corpus (1)

• Classification of Tensor Decompositions of II${}_1$ Factors Associated With Poly-Hyperbolic Groups