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Cyclotomic Integers, Fusion Categories, and Subfactors

Calegari, Frank; Morrison, Scott; Snyder, Noah

Description

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the Appendix...[Show more]

dc.contributor.authorCalegari, Frank
dc.contributor.authorMorrison, Scott
dc.contributor.authorSnyder, Noah
dc.date.accessioned2015-12-07T22:52:33Z
dc.identifier.issn0010-3616
dc.identifier.urihttp://hdl.handle.net/1885/27471
dc.description.abstractDimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the Appendix written by V. Ostrik, while the others are all realized by known examples. The second application proves that in any family of graphs obtained by adding a 2-valent tree to a fixed graph, either only finitely many graphs are principal graphs of subfactors or the family consists of the An or Dn Dynkin diagrams. This result is effective, and we apply it to several families arising in the classification of subfactors of index less than 5.
dc.publisherHarwood Academic Publishers
dc.sourceCommunications in Mathematical Physics
dc.titleCyclotomic Integers, Fusion Categories, and Subfactors
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume303
dc.date.issued2011
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.ariespublicationu4743872xPUB51
local.type.statusPublished Version
local.contributor.affiliationCalegari, Frank, Northwestern University
local.contributor.affiliationMorrison, Scott, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationSnyder, Noah, Columbia University
local.description.embargo2037-12-31
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage845
local.bibliographicCitation.lastpage896
local.identifier.doi10.1007/s00220-010-1136-2
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-07T12:30:43Z
local.identifier.scopusID2-s2.0-79953710537
local.identifier.thomsonID000289249700008
CollectionsANU Research Publications

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