<p dir="ltr">On this thesis, we study the validity of the Blackadar-Kirchberg conjecture for C*-<br>algebras that arise as extensions of separable, nuclear, quasidiagonal C*-algebras that satisfy<br>the Universal Coefficient Theorem. More specifically, we show that the conjecture for the<br>C*-algebra in the middle has an affirmative answer if the ideal lies in a class of C*-algebras<br>that is closed under local approximations and contains all separable ASH-algebras, as well<br>as certain classes of simple, unital C*-algebras and crossed products of unital C*-algebras<br>with Z. We also investigate when discrete, amenable groups have C*-algebras of real rank<br>zero. While it is known that this happens when the group is locally finite, the converse in<br>an open problem. We show that if C*(G) has real rank zero, then all normal subgroups of<br>G that are elementary amenable and have finite Hirsch length must be locally finite.<br><br></p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/26235275 |
| Date | 10 July 2024 |
| Creators | Iason Vasileios Moutzouris (18991658) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/FINITE_DIMENSIONAL_APPROXIMATIONS_OF_EXTENSIONS_OF_C_-ALGEBRAS_AND_ABSENCE_OF_NON-COMMUTATIVE_ZERO_DIMENSIONALITY_FOR_GROUP_C_-ALGEBRAS/26235275 |
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