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dc.contributor.authorSiehler, Jacob A.en
dc.date.accessioned2014-03-14T20:09:56Zen
dc.date.available2014-03-14T20:09:56Zen
dc.date.issued2003-04-18en
dc.identifier.otheretd-04182003-143702en
dc.identifier.urihttp://hdl.handle.net/10919/26962en
dc.description.abstractWe consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, for the existence or nonexistence of coherent associative structures for such fusion rules (ie, solutions to MacLane's pentagon equation). An explicit construction of matrix solutions to the pentagon equations is given for the cases where we establish existence, and classification of the distinct solutions is carried out partially. Many of these associative structures also support (braided) commutative and tortile structures and we indicate when the additional structures are possible. Small examples are presented in detail suitable for use in computational applications.en
dc.publisherVirginia Techen
dc.relation.haspartdissert.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmonoidal categoriesen
dc.subjectbraided categoriesen
dc.subjectquantum field theoryen
dc.titleNear-Group Categoriesen
dc.typeDissertationen
dc.contributor.departmentMathematicsen
dc.description.degreePh. D.en
thesis.degree.namePh. D.en
thesis.degree.leveldoctoralen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairQuinn, Frank S.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.committeememberGreen, Edward L.en
dc.contributor.committeememberHaskell, Peter E.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04182003-143702/en
dc.date.sdate2003-04-18en
dc.date.rdate2004-04-23en
dc.date.adate2003-04-23en


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