Selfless reduced amalgamated free products and HNN extensions
Operator Algebras
2026-04-29 v2 Group Theory
Logic
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.
Cite
@article{arxiv.2604.06982,
title = {Selfless reduced amalgamated free products and HNN extensions},
author = {David Gao and Srivatsav Kunnawalkam Elayavalli and Gregory Patchell and Lizzy Teryoshin},
journal= {arXiv preprint arXiv:2604.06982},
year = {2026}
}
Comments
v2: minor edits and fixes, cleaner proof of HNN theorem