Exactness of universal free products of finite dimensional $C^*$-algebras with amalgamation

TL;DR

This paper studies when free products of finite-dimensional $C^*$-algebras with amalgamation are exact or nuclear, providing conditions and descriptions to understand their structure better.

Contribution

It characterizes the exactness and nuclearity of free products of finite-dimensional $C^*$-algebras with amalgamation over diagonal subalgebras, offering new structural insights.

Findings

Identifies conditions for exactness of free products with amalgamation.

Provides descriptions of certain free products in terms of more understood algebras.

Clarifies when these free products are nuclear.

Abstract

We investigate free products of finite dimensional $C^*$-algebras with amalgamation over diagonal subalgebras. We look to determine under what circumstances a given free product is exact and/or nuclear. In some cases we find a description of the algebra in terms of a more readily understood algebra.