  A (finite or countably infinite) set G of generators of an abstract
C*-algebra A is called hyperrigid if for every faithful representation of A on
a Hilbert space $A\subseteq \mathcal B(H)$ and every sequence of unital
completely positive linear maps $\phi_1, \phi_2,...$ from $\mathcal B(H)$ to
itself,
  $$ \lim_{n\to\infty}\|\phi_n(g)-g\|=0, \forall g\in G \implies
\lim_{n\to\infty}\|\phi_n(a)-a\|=0, \forall a\in A. $$
  We show that one can determine whether a given set G of generators is
hyperrigid by examining the noncommutative Choquet boundary of the operator
space spanned by $G\cup G^*$. We present a variety of concrete applications and
discuss prospects for further development.
