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

We 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>. / Ph. D.

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38421
Date06 June 2008
CreatorsStoyanov, Ognyan S.
ContributorsMathematical Physics, Zweifel, Paul F., Greenberg, William, Haskell, Peter, Klaus, Martin, Bowden, Robert L., Kupershmidt, Boris, Slawny, Joseph
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeDissertation, Text
Formatv, 135 leaves, BTD, application/pdf, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationOCLC# 29323376, LD5655.V856_1993.S869.pdf

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