Non-Z-Stable Simple AH Algebras
| 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.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.identifier.uri | https://hdl.handle.net/1794/29070 | |
| 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.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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