Derivations on Murray–von Neumann algebras

This talk presents a full resolution of the problem stated by Ayupov in 2000 and partly restated in 2014 by Kadison and Liu. The talk consists of two parts and is based on a joint work with A.Ber.
The first part of the talk explains a background of the Ayupov–Kadison–Liu Problem and its connection with general derivation theory in operator algebras starting with fundamental results due to Kaplanski, Kadison, Sakai and others. We shall cite and briey explain major results concerning derivations on algebras of unbounded operators and list results concerning some special cases of the problem. Finally, the main result yielding the full resolution will be stated.
The second part of the talk will be concentrated on the explanation of the main ideas of the proof for finite von Neumann algebras of type II.