Subfactors of index less than 5, part 4: vines
Operator Algebras
2016-11-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1010.3797,
title = {Subfactors of index less than 5, part 4: vines},
author = {David Penneys and James E. Tener},
journal= {arXiv preprint arXiv:1010.3797},
year = {2016}
}
Comments
17 pages, many figures, minor changes from v1