(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups

Details (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups

1999-07-15

arxiv.org/abs/math/9907099v2

J.Phys. A 33 (2000) 3445-3465

Mathematics

Quantum Algebra

25 pages, LaTeX. Possible applications in relation with integrable systems are pointed; new references added

Scientific paper

10.1088/0305-4470/33/17/304

All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger 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 Schrodinger Poisson-Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and gl(2) Lie bialgebras within the Schrodinger classification are studied. As an application, new quantum (Hopf algebra) deformations of the Schrodinger algebra, including their corresponding quantum universal R-matrices, are constructed.

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