dc.contributor.advisor |
Lin, Huaxin |
|
dc.contributor.author |
Hendrickson, Allan |
|
dc.date.accessioned |
2024-01-09T21:06:31Z |
|
dc.date.available |
2024-01-09T21:06:31Z |
|
dc.date.issued |
2024-01-09 |
|
dc.identifier.uri |
https://scholarsbank.uoregon.edu/xmlui/handle/1794/29070 |
|
dc.description.abstract |
We consider the problem of dimension growth in AH algebras $A$ defined as inductive limits $A = \lim_{n \to \infty} (M_{R_n}(C(X_n)),\phi_{n})$ over finite connected CW-complexes $X_n$. We show that given any sequence $(X_n)$ of finite connected CW-complexes and matrix sizes $(R_n)$ with $R_n \rvert R_{n+1}$ satisfying the dimension growth condition $ \lim_{n \to \infty} \frac{\dim(X_n)}{R_n} = c$ with $c \in (0,\infty)$, there always exists an AH algebra with injective connecting homomorphisms over a subsequence which does not have Blackadar's strict comparison of positive elements, and therefore does not absorb tensorially the Jiang-Su algebra $Z$. This demonstrates that no regularity condition can be placed on the spaces $X_n$ in order to stabilize AH algebras over them - there always exists a pathological construction. |
en_US |
dc.language.iso |
en_US |
|
dc.publisher |
University of Oregon |
|
dc.rights |
All Rights Reserved. |
|
dc.subject |
AH algebra |
en_US |
dc.subject |
Elliott Invariant |
en_US |
dc.subject |
Radius of comparison |
en_US |
dc.subject |
Villadsen |
en_US |
dc.title |
Non-Z-Stable Simple AH Algebras |
|
dc.type |
Electronic Thesis or Dissertation |
|
thesis.degree.name |
Ph.D. |
|
thesis.degree.level |
doctoral |
|
thesis.degree.discipline |
Department of Mathematics |
|
thesis.degree.grantor |
University of Oregon |
|