II_1 Factors With a Unique McDuff Decomposition
We consider McDuff decompositions of II_1 factors. In particular, we will discuss a structural result for such a decomposition, when the central sequences of the non-McDuff part are captured by a Cartan subalgebra. This will allow us to deduce several new instances where the involved II_1 factor admits a unique McDuff decomposition. We will also comment on some related properties and results for equivalence relations.