In 1964, Tauer gave examples of countably many masas inside the hyperfinite II<sub>1</sub>von Neumann factor <i>R.</i> These masas were shown to be pairwise non-conjugate in <i>R</i> using a length invariant for the normalisers of semi-regular masas. A class of masas, the <i>Tauer masas,</i> is introduced consisting of all those masas obtained using her basic method of construction. The main body of this thesis is then concerned with examining the properties of these Tauer masas. In particular, the concepts of singularity, strong singularity and the weak asymptotic homomorphism property coincide for Tauer masas, and all Tauer mass have Pukánszky invariant {1}. Modern methods for calculating von Neumann algebras generated by normalisers are used to examine Tauer’s original examples, leading to shorter proofs of all of her results. Her initial example of a singular masa is studied in further detail. A generalisation of her semi-regular masas leads to the construction of an uncountable family of semi-regular masas of infinite length inside <i>R. </i>Examination of the Jones index of inclusions of the iterated normaliser algebras demonstrates that no pair of these masas can be conjugate by an automorphism of <i>R.</i> Centralising sequences for <i>R</i> lying inside masas are examined, with examples given to show that singular masas can be found containing non-trivial centralising sequences. An invariant, Γ(<i>A</i>), for a masa inside a II<sub>1</sub> factor is introduced as the size of a maximal cut-down for which the resulting masa contains non-trivial centralising sequences. This invariant is then used to exhibit a <i>d<sub>∞,</sub></i><sub>2</sub>-continuous path of uncountably many strongly singular masas in <i>R</i> with the same Pukánszky invariant, no pair of which is conjugate by an automorphism of <i>R.</i> Various issues arising from these concepts are discussed, such as possible masas in <i>R<sub>ω</sub></i> and the relationship between <i>A</i>-valued centralising sequences and automorphisms of <i>R</i> fixing <i>A</i> pointwise. Possible connections between this relative automorphism group and the Pukánskzy invariant will also be touched upon.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:663706 |
| Date | January 2005 |
| Creators | White, Stuart |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/11950 |
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