Covering dimension of Cuntz semigroups
| Autor: | Hannes Thiel, Eduard Vilalta |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Rank (linear algebra) Semigroup Mathematics::Operator Algebras General Mathematics 010102 general mathematics 05 social sciences Dimension (graph theory) Mathematics - Operator Algebras Zero (complex analysis) 01 natural sciences Primary 46L05 46L85 Secondary 54F45 55M10 Simple (abstract algebra) Mathematics::K-Theory and Homology Bounded function 0502 economics and business FOS: Mathematics 0101 mathematics Algebra over a field Operator Algebras (math.OA) 050203 business & management Mathematics |
| DOI: | 10.48550/arxiv.2101.04522 |
| Popis: | 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. Comment: 32 pages; extended introduction, added details on inductive limits and elements with thin boundary, rearranged order of results in Section 4; to appear in Adv. Math |
| Databáze: | OpenAIRE |
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