Semi-regular masas of transfinite length

Details Semi-regular masas of transfinite length Semi-regular masas of transfinite length

2006-11-20

arxiv.org/abs/math/0611615v1

Internat. J. Math. Vol. 18, No. 9 (2007) 995--1007

Mathematics

Operator Algebras

14 pages

Scientific paper

10.1142/S0129167X07004424

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.

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