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

• Autorzy: Angel Ballesteros , Mariano A. del Olmo
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 261-271

Daty

wydano

1997

Twórcy

autor

Angel Ballesteros

• Departamento de Física, Universidad de Burgos, E-09003, Burgos, Spain

autor

Mariano A. del Olmo

• Departamento de Física Teórica, Universidad de Valladolid, E-47011, Valladolid, Spain

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [7] E.J. Saletan, Contractions of Lie groups, J. Math. Phys 2 (1961), 1.
• [8] E. Weimar-Woods, The three-dimensional real Lie algebras and their contractions, J. Math. Phys 32 (1991), 2028.