COVERING DIMENSION FOR CUNTZ SEMIGROUPS

Speaker(s)

EDUARD VILALTA

Affiliation

Universitat Autònoma de Barcelona

Date

Dec. 1, 2021, 5:15 p.m.

Information about the event

ZOOM

Seminar

North Atlantic Noncommutative Geometry Seminar

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In this talk, I will present a notion of covering dimension for Cuntz semigroups and give an overview of the results found thus far. This dimension is always bounded by the nuclear dimension of the associated C*-algebra and, in the case of subhomogeneous C*-algebras, the two dimensions agree. For separable, simple, Z-stable C*-algebras, the Cuntz semigroup has dimension zero if and only if the algebra has real rank zero or is stably projectionless. I will also introduce a notion of approximation for abstract Cuntz semigroups and show that the property of having the covering dimension at most n is preserved by approximation. In particular, the covering dimension of the Cuntz semigroup of a C*-algebra is determined by the covering dimensions of the Cuntz semigroups of its separable C*-subalgebras. The talk is based on joint work with Hannes Thiel.

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