Subfactors of index less than 5, part 2: triple points

Details Subfactors of index less than 5, part 2: triple points Subfactors of index less than 5, part 2: triple points

2010-07-14

arxiv.org/abs/1007.2240v2

International Journal of Mathematics, Vol. 23, No. 3 (2012), 1250016

Mathematics

Operator Algebras

28 pages, many figures. Completely revised from v1: many additional or stronger results

Scientific paper

10.1142/S0129167X11007586

We summarize the known obstructions to subfactors with principal graphs which begin with a triple point. One is based on Jones's quadratic tangles techniques, although we apply it in a novel way. The other two are based on connections techniques; one due to Ocneanu, and the other previously unpublished, although likely known to Haagerup. We then apply these obstructions to the classification of subfactors with index below 5. In particular, we eliminate three of the five families of possible principal graphs called "weeds" in the classification from arXiv:1007.1730.

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