Quasidiagonality is a matricial approximation property which asymptotically captures the multiplicative structure of C* -algebras. Quasidiagonal C* -algebras must be stably finite. It has been conjectured by Blackadar and Kirchberg that stably finiteness implies quasidiagonality for the class of separable nuclear C* -algebras. It has also been conjectured that separable exact quasidiagonal C* -algebras are AF embeddable. In this thesis, we study the behavior of these conjectures in the context of extensions 0 → I → E → B → 0. Specifically, we show that if I is exact and connective and B is separable, nuclear, and quasidiagonal (AF embeddable), then E is quasidiagonal (AF embeddable). Additionally, we show that if I is of the form C(X) ⊗ K for a compact metrizable space X and B is separable, nuclear, quasidiagonal (AF embeddable), and satisfies the UCT, then E is quasidiagonal (AF embeddable) if and only if E is stably finite.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12735998 |
| Date | 30 July 2020 |
| Creators | Jacob R Desmond (9183335) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Quasidiagonal_Extensions_of_C_-algebras_and_Obstructions_in_K-theory/12735998 |
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