Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach.
@article{bwmeta1.element.bwnjournal-article-bcpv40z1p261bwm,
author = {Ballesteros, Angel and del Olmo, Mariano},
title = {Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {261-271},
zbl = {0890.17003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p261bwm}
}
Ballesteros, Angel; del Olmo, Mariano. Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations. Banach Center Publications, Tome 38 (1997) pp. 261-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p261bwm/
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