Subfactors of index less than 5, part 4: Vines
| dc.contributor.author | Penneys, David | en |
| dc.contributor.author | Tener, James E. | en |
| dc.date.accessioned | 2026-01-01T10:41:27Z | |
| dc.date.available | 2026-01-01T10:41:27Z | |
| dc.date.issued | 2012 | en |
| dc.description.abstract | We eliminate 39 infinite families of possible principal graphs as part of the classification of subfactors up to index 5. A number-theoretic result of CalegariMorrisonSnyder, 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 seven graphs in the index range (4,5) which actually occur as principal graphs. | en |
| dc.description.sponsorship | We would like to thank Scott Morrison, Emily Peters, and Noah Snyder for many helpful conversations, for proofreading the manuscript, and for useful programs in the FusionAtlas. We would also like to thank Vaughan Jones for hosting several Bodega Bay Planar Algebra Programming Camps. Both authors would like to acknowledge support from NSF grants DMS 0401734 and DMS 0856316 and from DOD-DARPA grant HR0011-11-1-0001. The second author was also supported by an NSF Graduate Research Fellowship. | en |
| dc.description.status | Peer-reviewed | en |
| dc.identifier.issn | 0129-167X | en |
| dc.identifier.scopus | 84858247528 | en |
| dc.identifier.uri | https://hdl.handle.net/1885/733799717 | |
| dc.language.iso | en | en |
| dc.source | International Journal of Mathematics | en |
| dc.subject | cyclotomic numbers | en |
| dc.subject | fusion categories | en |
| dc.subject | principal graphs | en |
| dc.subject | Subfactors | en |
| dc.title | Subfactors of index less than 5, part 4: Vines | en |
| dc.type | Journal article | en |
| dspace.entity.type | Publication | en |
| local.contributor.affiliation | Penneys, David; University of California at Berkeley | en |
| local.contributor.affiliation | Tener, James E.; University of California at Berkeley | en |
| local.identifier.citationvolume | 23 | en |
| local.identifier.doi | 10.1142/S0129167X11007641 | en |
| local.identifier.pure | 1c2db112-943d-4e97-ac82-a3f84230185a | en |
| local.identifier.url | https://www.scopus.com/pages/publications/84858247528 | en |
| local.type.status | Published | en |