Quasidiagonal Extensions Of C∗-Algebras and Obstructions in K-Theory
Abstract
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 nuclearC∗ -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 Eis quasidiagonal (AF embeddable) if and only if E is stably finite.
Degree
Ph.D.
Advisors
Dadarlat, Purdue University.
Subject Area
Mathematics
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