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Poisson-lie structures on infinite-dimensional jet groups and their quantization

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dc.contributor.authorStoyanov, Ognyan S.en
dc.contributor.committeecochairKupershmidt, Borisen
dc.contributor.committeecochairSlawny, Josephen
dc.contributor.committeememberZweifel, Paul F.en
dc.contributor.committeememberGreenberg, Williamen
dc.contributor.committeememberHaskell, Peteren
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberBowden, Robert L.en
dc.contributor.departmentMathematical Physicsen
dc.date.accessioned2014-03-14T21:14:19Zen
dc.date.adate2008-06-06en
dc.date.available2014-03-14T21:14:19Zen
dc.date.issued1993en
dc.date.rdate2008-06-06en
dc.date.sdate2008-06-06en
dc.description.abstractWe study the problem of classifying all Poisson-Lie structures on the group Gy of local diffeomorphisms of the real line R¹ which leave the origin fixed, as well as the extended group of diffeomorphisms G₀<sub>∞</sub> ⊃ G<sub>∞</sub> whose action on R¹ does not necessarily fix the origin. A complete classification of all Poisson-Lie structures on the group G<sub>∞</sub> is given. All Poisson-Lie structures of coboundary type on the group G₀<sub>∞</sub> are classified. This includes a classification of all Lie-bialgebra structures on the Lie algebra G<sub>∞</sub> of G<sub>∞</sub>, which we prove to be all of coboundary type, and a classification of all Lie-bialgebra structures of coboundary type on the Lie algebra Go<sub>∞</sub> of Go<sub>∞</sub> which is the Witt algebra. A large class of Poisson structures on the space V<sub>λ</sub> of λ-densities on the real line is found such that V<sub>λ</sub> becomes a homogeneous Poisson space under the action of the Poisson-Lie group G<sub>∞</sub>. We construct a series of finite-dimensional quantum groups whose quasiclassical limits are finite-dimensional Poisson-Lie factor groups of G<sub>∞</sub> and G₀<sub>∞</sub>.en
dc.description.degreePh. D.en
dc.format.extentv, 135 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06062008-170612en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06062008-170612/en
dc.identifier.urihttp://hdl.handle.net/10919/38421en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1993.S869.pdfen
dc.relation.isformatofOCLC# 29323376en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1993.S869en
dc.subject.lcshPoisson integral formulaen
dc.subject.lcshQuantum groupsen
dc.titlePoisson-lie structures on infinite-dimensional jet groups and their quantizationen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematical Physicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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