2 results
The admissible KMS bundles on classifiable C⁎-algebras
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 27 November 2024, pp. 1-34
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
Given any unital, finite, classifiable
$\mathrm{C}^*$-algebra A with real rank zero and any compact simplex bundle with the fibre at zero being homeomorphic to the space of tracial states on A, we show that there exists a flow on A realizing this simplex. Moreover, we show that given any unital 
$\mathrm{UCT}$ Kirchberg algebra A and any proper simplex bundle with empty fibre at zero, there exists a flow on A realizing this simplex.
Comparison Properties of the Cuntz Semigroup and Applications to C* -algebras
-
- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 26-52
- Print publication:
- 01 February 2018
-
- Article
-
- You have access
- Export citation
-
We study comparison properties in the category
$\text{Cu}$ aiming to lift results to the 
${{\text{C}}^{\text{*}}}$-algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property 
$\left( \text{CFP} \right)$ and 
$\omega $-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for ${{\text{C}}^{\text{*}}}$-algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear ${{\text{C}}^{\text{*}}}$-algebra with a finite and an inifnite projection does not have the 
$\text{CFP}$.
