Subfactors of index less than 5, part 4: vines

Details Subfactors of index less than 5, part 4: vines Subfactors of index less than 5, part 4: vines

2010-10-19

arxiv.org/abs/1010.3797v2

Mathematics

Operator Algebras

17 pages, many figures, minor changes from v1

Scientific paper

We eliminate 38 infinite families of possible principal graphs as part of the classification of subfactors up to index 5. A number-theoretic result of Calegari-Morrison-Snyder, generalizing Asaeda-Yasuda, reduces each infinite family to a finite number of cases. We provide algorithms for computing the effective constants that are required for this result, and we obtain 28 possible principal graphs. The Ostrik d-number test and an algebraic integer test reduce this list to 7 graphs in the index range (4,5) which actually occur as principal graphs.

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