Values of the Pukánszky invariant in McDuff factors

Abstract: In 1960 Pukánszky introduced an invariant associating to every masa in a separable II1 factor a non-empty subset of . 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 arises as the Pukánszky invariant of some masa in a separable McDuff II1 factor containing a masa with Pukánszky invariant . In particular the hyperfinite II1 factor and all separable McDuff II1 factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff factor we show that every subset of containing ∞ is obtained as a Pukánszky invariant of some masa. [Copyright &y& Elsevier]