Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them

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dc.creatorStoyanov, Ognyan
dc.date1995-06-08
dc.date.accessioned2026-07-07T09:16:35Z
dc.date.available2026-07-07T09:16:35Z
dc.descriptionWe study the problem of classifying all Poisson-Lie structures on the group $G_{\infty}$ of formal diffeomorphisms of the real line $\zR^{1}$ which leave the origin fixed, as well as the extended group of diffeomorphisms $G_{0\infty}\supset G_{\infty}$ whose action on $\zR^{1}$ does not necessarily fix the origin. A complete local classification of all Poisson-Lie structures on the groups $G_{\infty}$ and $G_{0\infty}$ is given. This includes a classification of all Lie-bialgebra structures on the Lie algebra $\Cal G_{\infty}$ of $G_{\infty}$, which we prove to be all of coboundary type, and a classification of all Lie-bialgebra strucutures on the Lie algebra $\Cal G_{0\infty}$ (the Witt algebra) of $G_{0\infty}$ which also turned out to be all of coboundary type. 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 $G_{\infty}$. We construct a series of quantum semigroups whose quasiclassical limits are finite-dimensional Poisson-Lie factor groups of $G_{\infty}$ and $G_{0\infty}$.
dc.description79 pages, AmSTeX file
dc.identifierhttps://arxiv.org/abs/q-alg/9506008
dc.identifierhttp://arxiv.org/abs/q-alg/9506008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153402
dc.subjectQuantum Algebra
dc.titlePoisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them
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