Quasidiagonality of Nuclear C*-Algebras

Specialeforsvar ved Mikkel Munkholm

Titel: Quasidiagonality of Nuclear $C^*$-Algebras

Abstract: The thesis investigates the impact of quasidiagonality on the classification programme, the programme being the attempt to classify nuclear separable simple unital $C^*$-algebras fulfilling the UCT-condition. The programme achieved prominent progress during the last couple of decades, and finally culminated into the classification theorem in the finite nuclear dimensional case. The theorem, however, assumed quasidiagonality of all traces on the aforementioned type of $C^*$-algebras. The thesis specifically pursues the proof of this particular assumption being automatic, a deep theorem due to Aaron Tikuisis, Stuart White and Wilhelm Winter in 2015. This includes an in depth analysis of quasidiagonality in the nuclear separable framework in terms of ultrapowers, von Neumann algebras induced from traces of such $C^*$-algebras, $KK$-theory of nuclear $C^*$-algebras and comparison theory. Towards the end, the connections between the Tikuisis-White-Winter theorem and the classification programme, the Blackadar-Kirchberg problem alongside the Rosenberg conjecture are provided.

Vejleder: Mikael Rørdam
Censor:   Wojciech Szymanski, SDU