A Kurosh type theorem for type II_1 factors

TL;DR

This paper establishes a Kurosh type theorem for free-product type II_1 factors, demonstrating their primeness and non-isomorphism, advancing the understanding of their structural properties.

Contribution

It introduces a Kurosh type theorem for free-product type II_1 factors, showing their primeness and pairwise non-isomorphism, extending previous results in the field.

Findings

All free-product type II_1 factors constructed from LF_2  R are prime.

These factors are pairwise non-isomorphic.

The work extends prior prime factorization results for type II_1 factors.

Abstract

We prove a Kurosh type theorem for free-product type II_1 factors. In particular, if M = LF_2 \otimes R, then the free-product type II_1 factors M*...*M are all prime and pairwise non-isomorphic. This paper is a continuation of [N. Ozawa, Solid von Neumann algebras] and [N. Ozawa and S. Popa, Some prime factorization results for type II_1 factors].