Divisibility properties for C*‐algebras
By Leonel Robert, M. Rørdam. 2011
55 citations recorded by the source corpus.
We consider three notions of divisibility in the Cuntz semigroup of a C*‐algebra, and show how they reflect properties of the C*‐algebra. We develop methods to construct (simple and non‐simple) C*‐algebras with specific divisibility behaviour. As a byproduct of our investigations, we show that there exists a sequence (An) of simple unital infinite dimensional C*‐algebras such that the product ∏n=1∞ An has a character.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/295a94b8ef49fd202b32dabbc0dbc29758504ca4
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- C*-algebras of stable rank one and their Cuntz semigroups (2018, unknown): “vely whenever A has Hausdorff, finite dimensional, primitive ideal space (see [BK04a, Theorem 4.3]), and whenever A is a C*-algebra with real rank zero ([ER06]). The problem remains open in general. In [RR13], the Global Glimm Halving Problem is translated into an equivalence of divisibility propertie”
- Tensor products and regularity properties of Cuntz semigroups (2014, unknown): “1142/S0129167X04002661 [83] Robert, Leonel; Rørdam, Mikael, Divisibility properties for \(C^*\)-algebras, Proc.”
- The cone of functionals on the Cuntz semigroup (2011, methodology): “2] and it was also used repeatedly in the arguments of [11].”