Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations

Volume 40 / 1997

Angel Ballesteros, Mariano del Olmo Banach Center Publications 40 (1997), 261-271 DOI: 10.4064/-40-1-261-271

Abstract

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.

Authors

  • Angel Ballesteros
  • Mariano del Olmo

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