Lie Bialgebra Structures on Twodimensional Galilei Algebra and Their Lie–poisson Counterparts
نویسنده
چکیده
All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie–Poisson structures on Galilei group are found. ∗Supported by the Lódź University Grant No.487
منابع مشابه
Schrödinger Lie bialgebras and their Poisson – Lie groups
All Lie bialgebra structures for the (1+ 1)-dimensional centrally extended Schrödinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrödinger Poisson–Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and g...
متن کاملLie bialgebra quantizations of the oscillator algebra and their universal R – matrices
All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.
متن کاملSome Remarks on the Classification of Poisson
We describe some results in the problem of classifying the bialgebra structures on a given nite dimensional Lie algebra. We consider two aspects of this problem. One is to see which Lie algebras arise (up to isomorphism) as the big algebra in a Manin triple, and the other is to try and determine all the exact Poisson structures for a given semisimple Lie algebra. We follow here the presentation...
متن کاملun 1 99 6 Lie bialgebra quantizations of the oscillator algebra and their universal R – matrices
All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.
متن کاملJu n 20 00 Poisson – Lie structures on Galilei group ∗
The complete list of Poisson–Lie structures on 4-d Galilei group is presented.
متن کامل