Groups of isometries of the Cuntz algebras

Abstract

We provide a new interpretation of the group of Bogolubov automorphisms of the Cuntz algebras ${\mathcal{O}}_n$ and the group $\mathrm{Aut}({\mathcal{O}}_n,{\mathcal{F}}_n)$ of all automorphisms preserving the UHF subalgebra ${\mathcal{F}}_n\subset {\mathcal{O}}_n$ as the isometry groups coming from two distinct spectral triples on ${\mathcal{O}}_n$.