Wednesday, January 23, 2019 — 3:30 PM EST

Guy Salomon, Department of Pure Mathematics, University of Waterloo

"Hyperrigid subsets of Cuntz–Krieger algebras and the property of rigidity at zero”

A generating set of a C*-algebra is said to be hyperrigid if for every faithful nondegenerate *-representation of the C*-algebra on a Hilbert space H, every sequence of unital completely positive self maps of B(H) that converges to the identity on the generating set, converges to the identity on the whole C*-algebra (all convergences are in the pointwise-norm sense). I will show that inside the Cuntz–Krieger algebra of a row-finite directed graph with no isolated vertices, the set of all edge partial-isometries is hyperrigid. I will also present, both in general and in the graph context, a related property called rigidity at zero that sheds light on the phenomenon of hyperrigidity.

MC 5417

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