FINITE DIMENSIONAL APPROXIMATIONS OF EXTENSIONS OF C*-ALGEBRAS AND ABSENCE OF NON-COMMUTATIVE ZERO DIMENSIONALITY FOR GROUP C*-ALGEBRAS

On this thesis, we study the validity of the Blackadar-Kirchberg conjecture for C*-
algebras that arise as extensions of separable, nuclear, quasidiagonal C*-algebras that satisfy
the Universal Coefficient Theorem. More specifically, we show that the conjecture for the
C*-algebra in the middle has an affirmative answer if the ideal lies in a class of C*-algebras
that is closed under local approximations and contains all separable ASH-algebras, as well
as certain classes of simple, unital C*-algebras and crossed products of unital C*-algebras
with Z. We also investigate when discrete, amenable groups have C*-algebras of real rank
zero. While it is known that this happens when the group is locally finite, the converse in
an open problem. We show that if C*(G) has real rank zero, then all normal subgroups of
G that are elementary amenable and have finite Hirsch length must be locally finite.