Values of the Pukánszky invariant in McDuff factors

In 1960 Pukánszky introduced an invariant associating to every masa in a separable II1 factor a nonempty subset of N ∪ {∞}. This invariant examines the multiplicity structure of the von Neumann algebra generated by the left-right action of the masa. In this paper it is shown that any non-empty subset of N∪{∞} arises as the Pukánszky invariant of some masa in a separable McDuff II1 factor containing a masa with Pukánszky invariant {1}. In particular the hyperfinite II1 factor and all separable McDuff II1 factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff II1 factor we show that every subset of N ∪ {∞} containing∞is obtained as a Pukánszky invariant of some masa. © 2007 Elsevier Inc. All rights reserved.