Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G×G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns out to be the well known $π _{+}$). We analyze the same condition in the context of Hopf algebras. A quantum analogue of the $π _{+}$ structure on SU(N) is described in terms of generators and relations as an example.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
273-278
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
- Department of Mathematical Methods in Physics, University of Warsaw, Hoża 74, 00-682 Warszawa, Poland
Bibliografia
- [1] V. G. Drinfeld, Hamiltonian structures on Lie groups, Lie bialgebras and the meaning of the classical Yang-Baxter equations, Soviet Math. Dokl. 27 (1983), 68-71.
- [2] V. G. Drinfeld, Quantum groups, Proc. ICM, Berkeley, 1986, vol.1, 789-820.
- [3] M. A. Semenov-Tian-Shansky, Dressing transformations and Poisson Lie group actions, Publ. Res. Inst. Math. Sci., Kyoto University 21 (1985), 1237-1260.
- [4] J.-H. Lu and A. Weinstein, Poisson Lie Groups, Dressing Transformations and Bruhat Decompositions, J. Diff. Geom. 31 (1990), 501-526.
- [5] J.-H. Lu, Multiplicative and affine Poisson structures on Lie groups, Ph.D. Thesis, University of California, Berkeley (1990).
- [6] S. Zakrzewski, Poisson structures on the Lorentz group, Lett. Math. Phys. 32 (1994), 11-23.
- [7] S. Zakrzewski, 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.), Polish Scientific Publishers PWN, Warsaw 1995, pp. 629-639.
- [8] S. L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), 35.
- [9] J.-H. Lu, On the Drinfeld double and the Heisenberg double of a Hopf algebra, Duke Math. Journ. 74, No.3 (1994), 763-776.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv40z1p273bwm