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_∞ ⊃ G_∞ whose action on R¹ does not necessarily fix the origin. A complete classification of all Poisson-Lie structures on the group G_∞ is given. All Poisson-Lie structures of coboundary type on the group G₀_∞ are classified. This includes a classification of all Lie-bialgebra structures on the Lie algebra G_∞ of G_∞, 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_∞ of Go_∞ which is the Witt algebra. A large class of Poisson structures on the space V_λ of λ-densities on the real line is found such that V_λ becomes a homogeneous Poisson space under the action of the Poisson-Lie group G_∞. We construct a series of finite-dimensional quantum groups whose quasiclassical limits are finite-dimensional Poisson-Lie factor groups of G_∞ and G₀_∞.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematical Physics

Department dc:contributor.department

Mathematical Physics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1993

Author dc:creator

• Stoyanov, Ognyan S.

Chairs dc:contributor.committeechair

• Kupershmidt, Boris
• Slawny, Joseph

Committee members dc:contributor.committeemember

• Zweifel, Paul F.
• Greenberg, William
• Haskell, Peter
• Klaus, Martin
• Bowden, Robert L.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-06062008-170612

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38421