2021/01/12 by Thiel, Hannes, Vilalta, Eduard
#46L85 #55M10 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 54F45
paper · doi:10.48550/arxiv.2101.04522
We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous C*-algebras both dimensions agree. Cuntz semigroups of Z-stable C*-algebras have dimension at most one. Further, the Cuntz semigroup of a simple, Z-stable C*-algebra is zero-dimensional if and only if the C*-algebra has real rank zero or is stably projectionless.