New Examples of Irreducible Subfactors of the Hyperfinite II1 Factor with Rational, Non-Integer Index
dc.contributor.advisor | Bisch, Dietmar | |
dc.creator | Stojanovic, Hrvoje | |
dc.date.accessioned | 2022-01-10T16:46:07Z | |
dc.date.available | 2022-01-10T16:46:07Z | |
dc.date.created | 2021-12 | |
dc.date.issued | 2021-11-02 | |
dc.date.submitted | December 2021 | |
dc.identifier.uri | http://hdl.handle.net/1803/16972 | |
dc.description.abstract | In his thesis, Schou showed that certain infinite-dimensional commuting squares could be used to construct irreducible hyperfinite subfactors. Bisch used this approach to construct a subfactor with index 4.5 that was the first example of an irreducible hyperfinite subfactor with rational, non-integer index. In this dissertation, we construct new examples of irreducible hyperfinite subfactors with rational, non-integer index. We first show that, for every N ≥ 4, if there exists a symmetric commuting square based on an inclusion graph N-star with A_∞-tail, the resulting irreducible hyperfinite subfactor would have a rational, non-integer index. We then explicitly construct such symmetric commuting squares in the case N = 5, 6, 7 and 9. Thus, there exist irreducible hyperfinite subfactors based on N-stars with A_∞-tail for these N, and their indices are 5 + 1/3, 6 + 1/4, 7 + 1/5 and 9 + 1/7. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | commuting squares | |
dc.subject | subfactors | |
dc.subject | von Neumann algebras | |
dc.title | New Examples of Irreducible Subfactors of the Hyperfinite II1 Factor with Rational, Non-Integer Index | |
dc.type | Thesis | |
dc.date.updated | 2022-01-10T16:46:07Z | |
dc.type.material | text | |
thesis.degree.name | PhD | |
thesis.degree.level | Doctoral | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University Graduate School | |
dc.creator.orcid | 0000-0002-5244-6181 | |
dc.contributor.committeeChair | Bisch, Dietmar |
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