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Categorified Uq(sl2)-theory using Bar-Natan’s approach

dc.contributor.advisorStroppel, Catharina
dc.contributor.authorSchäfer, Gisa
dc.date.accessioned2020-04-19T22:58:58Z
dc.date.available2020-04-19T22:58:58Z
dc.date.issued18.06.2014
dc.identifier.urihttps://hdl.handle.net/20.500.11811/6107
dc.description.abstractFor V the Uq(sl2)-module which is the quantum version of the natural representation, we categorify the n-fold tensor product of V as a module over the Temperley-Lieb algebra. To do this, we use Bar-Natan's approach of categorifying the Temperley-Lieb algebra to categorify the weight spaces of the n-fold tensor product of V with the canonical basis. The standard basis and the dual standard basis is then categorified by constructing chain complexes in the homotopy category. After that, we consider chain maps between the categorified dual standard basis elements to construct a special chain complex containing all of them, on which the categorified Temperley-Lieb algebra acts trivially. This special complex is then used to construct functors that satisfy the conditions of the projection and inclusion, which compose to the Jones-Wenzl projector, on a higher level.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleCategorified Uq(sl2)-theory using Bar-Natan’s approach
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-36408
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID3640
ulbbnediss.date.accepted03.06.2014
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeBödigheimer, Carl-Friedrich


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