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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38421 |
| Date | 06 June 2008 |
| Creators | Stoyanov, Ognyan S. |
| Contributors | Mathematical Physics, Zweifel, Paul F., Greenberg, William, Haskell, Peter, Klaus, Martin, Bowden, Robert L., Kupershmidt, Boris, Slawny, Joseph |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 135 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 29323376, LD5655.V856_1993.S869.pdf |
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