Hyperrigid subsets of Cuntz-Krieger algebras and the property of rigidity at zero

Abstract

Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Summary: A subset G generating a C∗-algebra A is said to be \textit{hyperrigid} if for every faithful nondegenerate ∗-representation A⊆B(H) and a sequence ϕn:B(H)→B(H) of unital completely positive maps, we have that limn→∞ϕn(g)=gfor all g∈G⟹limn→∞ϕn(a)=afor all a∈A. We show that in the Cuntz-Krieger algebra of a row-finite directed graph with no isolated vertices, the set of all edge partial-isometries is hyperrigid. We also examine, both in general and in the context of graphs, a related property named \textit{rigidity at} 0 that sheds light on the phenomenon of hyperrigidity.