Mathematics – Quantum Algebra
Scientific paper
1995-06-08
Mathematics
Quantum Algebra
79 pages, AmSTeX file
Scientific paper
We 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 $V_{\lambda}$ of $\lambda$-densities on the real line is found such that $V_{\lambda}$ 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 $G_{0\infty}$.
Stoyanov Ognyan
No associations
LandOfFree
Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-360035