W*-rigidity paradigms for embeddings of II1 factors
MATHEMATICAL PICTURE LANGUAGE
Stefaan Vaes - Katholieke Universiteit Leuven
I will report on a recent joint work with Sorin Popa in which we undertake a systematic study of W*-rigidity paradigms for the embedding relation between II1 factors and their amplifications. We say that a II1factor M stably embeds into a II1 factor N if M may be realized as a subfactor of an amplification of N, not necessarily of finite index. This is a preorder relation and we prove that it is as complicated as it can be: under the appropriate separability assumptions, we concretely realize any partially ordered set inside the preordered class of II1 factors with embeddability.