## Semiregular masas of transfinite length

*Abstract:* In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.

### Publication Details

*Coauthors:* Alan Wiggins

Internat. J. Math. 18 (2007) 995--1007. DOI: 10.1142/S0129167X07004424

*Download:* Journal Website, arXiv.math:0611615.

The version on the arXiv perpetuates the unfortunate error that the Fourier series used to approximate the crossed product can be made to converge in strong-topology. In fact this convergence only occurs in 2-norm. We are greatful to the referee for pointing this out, and this error is avoided in the published version.

## Wall Street

A fleeting visit to New York, January 2009.