All Questions

For $1\leq i\leq n$, let $\psi_i$ be a faithful state on the C$^*$-algebra $A_i$ and $\phi_i$ be a faithful state on the C$^*$-algebra $B_i$. Let $(A,\psi) = *_{i=1}^n (A_i,\psi_i)$ and $(B, \phi) = *...

It was shown by Pimsner and Voiculescu in 1982 that the reduced group $C^{*}$-algebras $C^{*}_{r}(\mathbb{F}_{n})$ and $C^{*}_{r}(\mathbb{F}_{m})$ are isomorphic if and only if $n = m$ (here, $\mathbb{...