Semi-regular masas of transfinite length

White, S.A. and Wiggins, A.D. (2007) Semi-regular masas of transfinite length. International Journal of Mathematics, 18(9), pp. 995-1007. (doi: 10.1142/S0129167X07004424)

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Publisher's URL: http://dx.doi.org/10.1142/S0129167X07004424

Abstract

In 1965, Tauer produced a countably infinite family of semi-regular masas in the hyperfinite II1 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 normalizers and, for each n ∈ ℕ, finding masas for which this procedure terminates at the nth 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 II1 factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalizing tower.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: White, S.A., and Wiggins, A.D.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Journal of Mathematics
Journal Abbr.:IJM
ISSN:0129-167X
ISSN (Online):1793-6519

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