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Categories generated by a trivalent vertex

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Morrison, Scott; Peters, Emily; Snyder, Noah

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This is the first paper in a general program to automate skein theoretic arguments. In this paper, we study skein theoretic invariants of planar trivalent graphs. Equivalently, we classify trivalent categories, which are nondegenerate pivotal tensor categories over C generated by a symmetric self-dual simple object X and a rotationally invariant morphism 1 → X⊗X⊗X.

dc.contributor.authorMorrison, Scott
dc.contributor.authorPeters, Emily
dc.contributor.authorSnyder, Noah
dc.date.accessioned2021-05-20T00:45:39Z
dc.identifier.issn1022-1824
dc.identifier.urihttp://hdl.handle.net/1885/233371
dc.description.abstractThis is the first paper in a general program to automate skein theoretic arguments. In this paper, we study skein theoretic invariants of planar trivalent graphs. Equivalently, we classify trivalent categories, which are nondegenerate pivotal tensor categories over C generated by a symmetric self-dual simple object X and a rotationally invariant morphism 1 → X⊗X⊗X.
dc.description.sponsorshipScott Morrison was supported by an Australian Research Council Discovery Early Career Researcher Award DE120100232, and Discovery Projects DP140100732 and DP160103479. Emily Peters was supported by the NSF Grant DMS-1501116. Noah Snyder was supported by the NSF Grant DMS-1454767. All three authors were supported by DOD-DARPA Grant HR0011-12-1-0009.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherSpringer Verlag
dc.rights© Springer International Publishing 2016
dc.sourceSelecta Mathematica
dc.subject18D10 (Monoidal Categories)
dc.subject05C10 (Planar graphs; geometric and topological aspects of graph theory)
dc.subject57M27 (Invariants of knots and 3-manifolds)
dc.titleCategories generated by a trivalent vertex
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume23
dc.date.issued2017
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.absfor010108 - Operator Algebras and Functional Analysis
local.identifier.absfor010112 - Topology
local.identifier.ariespublicationU3488905xPUB24290
local.publisher.urlhttps://link.springer.com/
local.type.statusAccepted Version
local.contributor.affiliationMorrison, Scott, College of Science, ANU
local.contributor.affiliationPeters, Emily, Loyola University Chicago
local.contributor.affiliationSnyder, Noah, Indiana University
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage817
local.bibliographicCitation.lastpage868
local.identifier.doi10.1007/s00029-016-0240-3
dc.date.updated2020-11-23T10:17:49Z
local.identifier.scopusID2-s2.0-84978035498
local.identifier.thomsonID000398491700001
dcterms.accessRightsOpen Access
dc.relation.urihttp://purl.org/au-research/grants/arc/DE120100232
dc.relation.urihttp://purl.org/au-research/grants/arc/DP140100732
dc.relation.urihttp://purl.org/au-research/grants/arc/DP160103479
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/14493..."Author Accepted Manuscript can be made open access on institutional repository after 12 month embargo" from SHERPA/RoMEO site (as at 16.9.2021).
CollectionsANU Research Publications

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