Boundary rigidity for free product C*-algebras

TL;DR

This paper establishes a boundary rigidity result for reduced free product C*-algebras, leading to new examples of rigid embeddings into purely infinite simple nuclear C*-algebras.

Contribution

It introduces a boundary rigidity theorem for free product C*-algebras and demonstrates their rigid embedding into purely infinite simple nuclear C*-algebras.

Findings

Proves boundary rigidity for free product C*-algebras

Provides new examples of rigid embeddings

Shows embeddings into purely infinite simple nuclear C*-algebras

Abstract

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A, \varphi)$. This provides new examples of rigid embeddings of exact $\mathrm{C}^*$-algebras into purely infinite simple nuclear $\mathrm{C}^*$-algebras.