Poisson structures on Poincaré group

Communications in Mathematical Physics

Volumn 185, Issue 2, 1997, Pages 285-311

  Zakrzewski, S ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031138533     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050091     Document Type: Article

References (20)

1. Zakrzewski, S.: Poisson Poincaré groups. In: "Quantum Groups, Formalism and Applications". Proceedings of the XXX Winter School on Theoretical Physics 14-26 February 1994, Karpacz, J. Lukierski, Z. Popowicz, J. Sobczyk (eds.), Warsaw: Polish Scientific Publishers PWN, 1995, pp. 433-439 (also: hep-th/94I2099)
2. Podles, P. and Woronowicz, S.L.: On the classification of quantum Poincaré groups. Commun. Math. Phys. 178, 61 (1996)
3. Greub, W., Halperin, S. and Van Stone, R.: Curvature. Connection and Cohomology. Pure and Applied Mathematics, Vol. 47, III, New York: Academic Press, 1976
4. Drinfeld, V. G.: Hamiltonian structures on Lie groups, Lie bialgebras and the meaning of the classical Yang-Baxter equations. Soviet Math. Dokl. 27, 68-71 (1983)
5. Drinfeld, V. G.: Quantum groups. Proc. ICM, Berkeley, 1986, Vol. 1, pp. 789-820
6. Semenov-Tian-Shansky, M. A.: Dressing transformations and Poisson Lie group actions. Publ. Res. Inst. Math. Sci., Kyoto University 21, 1237-1260 (1985)
7. Lu, J.-H. and Weinstein, A.: Poisson Lie Groups. Dressing Transformations and Bruhat Decompositions. J. Diff. Geom. 31, 501-526 (1990)
8. Bourbaki, N.: Groupes et algèbres de Lie. Chapitre VIII, Paris: Hermann, 1975
9. Podleś, P. and Woronowicz, S.L.: On the structure of inhomogeneous quantum groups, hep-th/9412058. To appear in Commun. Math. Phys.
10. Zakrzewski, S.: Geometric quantization of Poisson groups - Diagonal and soft deformations. Proceedings of the Taniguchi Symposium Symplectic geometry and quantization problems, Sanda (1993), Y. Maeda, H. Omori and A. Weinstein (eds.), Contemp. Math. 179, 271-285 (1994)
11. Zakrzewski, S.: Poisson structures on the Lorentz group. Lett. Math. Phys. 32, 11-23 (1994)
12. Zakrzewski, S.: Quantum Poincaré group related to κ-Poincaré algebra. J. Phys. A: Math. Gen. 27, 2075-2082 (1994)
13. Belavin, A. and Drinfeld, V.G.: Triangle equations and simple Lie algebras. Sov. Sci. Rev. Math. 4, 93-165 (1984)
14. Zakrzewski, S.: Poisson space-time symmetry and corresponding elementary systems. In: "Quantum Symmetries", Proceedings of the II International Wigner Symposium, Goslar 1991, H.D. Doebner and V.K. Dobrev (Eds.), pp. 111-123
15. Stachura. P.: Poisson structures on Poincaré and Euclidean groups in 3 dimensions, preprint Warsaw 1997
16. Zakrzewski, S.: Poisson homogeneous spaces. In: "Quantum Groups, Formalism and Applications", Proceedings of the XXX Winter School on Theoretical Physics, 14-26 February 1994, Karpacz, J. Lukierski, Z. Popowicz, J. Sobczyk (eds.), Warsaw: Polish Scientific Publishers PWN, 1995, pp. 629-639 (also hep-th/9412101)
17. Zakrzewski, S.: Phase spaces related to standard classical r-matrices. J. Phys. A: Math. Gen. 29, 1841 (1996)
18. Zakrzewski, S.: Poisson Poincaré particle and canonical variables. In: "Generalized Symmetries", Proceedings of the International Symposium on Mathematical Physics, Clausthal, July 27-29, 1993, H.-D. Doebner, V.K. Dobrev and A.G. Ushveridze (Eds.), 1994, pp. 165-171
19. Zakrzewski, S.: On the classical κ-particle In: "Quantum Groups, Formalism and Applications", Proceedings of the XXX Winter School on Theoretical Physics, 14-26 February 1994, Karpacz, J. Lukierski, Z. Popowicz, J. Sobczyk (eds.), Warsaw: Polish Scientific Publishers PWN, 1995, pp. 573-577 (also: hep-th/9412098)
20. Zakrzewski, S.: Classical mechanical systems based on Poisson symmetry. Submitted for the Proceedings of the Second German-Polish Symposium "New Ideas in the Theory of Fundamental Interactions", September 1995, Zakopane, Poland