Selfless reduced amalgamated free products and HNN extensions

TL;DR

This paper introduces a broad family of selfless inclusions in reduced amalgamated free products of C*-algebras, providing new methods and examples, and extending previous results in the field.

Contribution

It generalizes prior work on selflessness in C*-algebras, offers a new approach to constructing HNN extensions, and applies these to graph products.

Findings

Established a family of selfless inclusions in free products of C*-algebras.

Provided a new method for constructing HNN extensions of C*-algebras.

Proved selflessness for graph products over complex graphs.

Abstract

We find a general family of selfless inclusions in reduced amalgamated free products of C*-algebras. Apart from generalizing prior works due to McClanahan, Ivanov and Omland, our work yields a few other applications. We present a short new approach to construct HNN extensions of C*-algebras and find several new examples of selflessness using this. This generalizes results of Ueda, Ivanov and de la Harpe-Preaux. As another application our work yields a short proof of selflessness for arbitrary graph products of C*-algebras over graphs of more than 2 vertices and diameter greater than 3.