On certain free product factors via an extended matrix model

TL;DR

This paper extends Voiculescu's random matrix model to non-Gaussian and block diagonal cases, enabling analysis of free products of free group factors with matrix algebras and hyperfinite factors, revealing new algebraic identities.

Contribution

It introduces an extended matrix model for free probability, allowing new insights into free product factors involving matrix and hyperfinite algebras.

Findings

Proves that L(F_n) * R = L(F_{n+1}) for n ≥ 1

Extends free probability models to non-Gaussian and block diagonal matrices

Provides new tools for analyzing free product factors

Abstract

Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the hyperfinite II$_1$ factor, showing that $$ L(F_n) * R = L(F_(n+1)) $$ for $n \ge 1$, (where $L(F_1)=L(Z)$).