Boundary rigidity for free product C*-algebras

Abstract

For any reduced free product ${\mathrm{C}}^{\ast }$-algebra $(A,\phi )=(A_1,{\phi }_1)\star (A_2,{\phi }_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated ${\mathrm{C}}^{\ast }$-algebra $\Delta \mathbf{T}(A,\phi )$. This provides new examples of rigid embeddings of exact ${\mathrm{C}}^{\ast }$-algebras into purely infinite simple nuclear ${\mathrm{C}}^{\ast }$-algebras.

8 pages

References in corpus (2)

• C*-simplicity and the unique trace property for discrete groups
• Boundaries of reduced C*-algebras of discrete groups