|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Recovering the Elliott invariant from the Cuntz semigroup | | Ramon Antoine
; Marius Dadarlat
; Francesc Perera
; Luis Santiago
; | | Date: |
27 Sep 2011 | | Abstract: | Let $A$ be a simple, separable C$^*$-algebra of stable rank one. We prove
that the Cuntz semigroup of $CC(T,A)$ is determined by its Murray-von Neumann
semigroup of projections and a certain semigroup of lower semicontinuous
functions (with values in the Cuntz semigroup of $A$). This result has two
consequences. First, specializing to the case that $A$ is simple, finite,
separable and $mathcal Z$-stable, this yields a description of the Cuntz
semigroup of $CC(T,A)$ in terms of the Elliott invariant of $A$. Second,
suitably interpreted, it shows that the Elliott functor and the functor defined
by the Cuntz semigroup of the tensor product with the algebra of continuous
functions on the circle are naturally equivalent. | | Source: | arXiv, 1109.5803 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER