Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations
Angel Ballesteros; Mariano del Olmo
Banach Center Publications (1997)
- Volume: 40, Issue: 1, page 261-271
- ISSN: 0137-6934
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topBallesteros, Angel, and del Olmo, Mariano. "Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations." Banach Center Publications 40.1 (1997): 261-271. <http://eudml.org/doc/252186>.
@article{Ballesteros1997,
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.},
author = {Ballesteros, Angel, del Olmo, Mariano},
journal = {Banach Center Publications},
keywords = {contractions of Poisson-Lie groups; Lie bialgebra contractions},
language = {eng},
number = {1},
pages = {261-271},
title = {Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations},
url = {http://eudml.org/doc/252186},
volume = {40},
year = {1997},
}
TY - JOUR
AU - Ballesteros, Angel
AU - del Olmo, Mariano
TI - Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 261
EP - 271
AB - 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.
LA - eng
KW - contractions of Poisson-Lie groups; Lie bialgebra contractions
UR - http://eudml.org/doc/252186
ER -
References
top- [1] A. Ballesteros, Contractions of Lie bialgebras and quantum deformations of kinematical symmetries, Ph. D. Thesis (in Spanish), Universidad de Valladolid (1995).
- [2] A. Ballesteros, N.A. Gromov, F.J. Herranz, M.A. del Olmo and M. Santander, Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras, J. Math. Phys. 36 (1995), 5916. Zbl0868.17012
- [3] A. Ballesteros, F.J. Herranz, C.M. Pereña, M.A. del Olmo and M. Santander, Non standard quantum (1+1) Poincaré group: a T matrix approach, J. Phys. A: Math. Gen. 28 (1995), 7113. Zbl0885.17012
- [4] E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, Contractions of quantum groups, Lecture Notes in Mathematics n. 1510. Springer-Verlag, Berlín (1992) 221. Zbl0757.17011
- [5] V.G. Drinfel'd, Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations, Sov. Math. Dokl. 27 (1983), 68.
- [6] E. Inönü and E.P. Wigner, Contractions of groups and representations, Proc. Natl. Acad. Sci. U. S. 39 (1953), 510. Zbl0050.02601
- [7] E.J. Saletan, Contractions of Lie groups, J. Math. Phys 2 (1961), 1. Zbl0098.25804
- [8] E. Weimar-Woods, The three-dimensional real Lie algebras and their contractions, J. Math. Phys 32 (1991), 2028. Zbl0751.17003
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