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

Simple item page
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

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LD5655.V856_1993.S869.pdf
Size:
5.28 MB
Format:
Adobe Portable Document Format
Description:
Download

Collections

Doctoral Dissertations