## Values of the Pukanszky invariant in McDuff Factors

*Abstract:* In 1960 Pukanszky introduced an invariant associating to every masa in a separable II_{1} factor a non-empty subset of N\cup{\infty}. 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 every non-empty subset of N\cup{\infty} arises as the Pukanszky invariant of some masa in a separable McDuff II_{1} factor which contains a masa with Puk\'anszky invariant {1}. In particular the hyperfinite II_{1} factor and all separable McDuff II_{1} factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff factor we show that every subset of N\cup{\infty} containing \infty is obtained as a Pukanskzy invariant of some masa.

### Publication Details

J. Funct. Anal. 254 (2008), no. 3, 612--631. DOI: 10.1016/j.jfa.2007.10.011

*Download:* Journal Website, arXiv.math:0609269, Glasgow ePrint 4611.

The arXiv and the Glasgow ePrint server are the versions accepted by JFA.

## Sella towers, Italy

An interesting crossing to gain the first Sella tower. July 2011.