Relative Embeddability of von Neumann Algebras and Amalgamated Free Products

TL;DR

This paper investigates conditions for embedding amalgamated free products of finite von Neumann algebras into ultrapowers of hyperfinite factors, advancing understanding of their structural properties.

Contribution

It introduces new criteria for the embeddability of reduced amalgamated free products of von Neumann algebras into ultrapowers of hyperfinite factors.

Findings

Identifies conditions for embeddability into ultrapowers

Establishes links between algebra inclusions and free product structures

Provides new insights into the structure of von Neumann algebra amalgamations

Abstract

In this paper we study conditions under which, for an inclusion of finite von Neumann algebras $N \subseteq M$, we have the reduced amalgamated free product $\ast_N M$ is embeddable into $(R \bar{\otimes} N_1)^\omega$ for some other finite von Neumann algebra $N_1$, where $R$ is the hyperfinite $\textrm{II}_1$ factor.