Finite dimensional approximations of certain amalgamated free products of groups

TL;DR

This paper introduces a new class of MF groups by demonstrating that amalgamated free products of two amenable groups with a common normal subgroup admit finite dimensional approximate unitary representations.

Contribution

It proves that certain amalgamated free products of amenable groups are MF, expanding the class of known MF groups.

Findings

Amalgamated free products of two amenable groups with a common normal subgroup are MF.

Provides new examples of MF groups.

Advances understanding of finite dimensional approximations in group theory.

Abstract

A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of MF groups by showing that given two amenable groups with a common normal subgroup, the amalgamated free product is MF.