Quantization of Co-Isotropic Subgroups
Article
- 61 Downloads
- 7 Citations
Abstract
The purpose of this Letter is to show that the concept of co-isotropic subgroups of a Poisson–Lie group can be given a natural analogue in the context of quantum homogeneous spaces, explaining some of the special features of this theory. We will give examples related to some previously known and some new quantum homogeneous spaces of the two-dimensional Euclidean quantum groups.
Poisson homogeneous spaces quantum homogeneous spaces Poisson subgroups quantum subgroups quantum quotients one sided ideas.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Bonechi, F., Ciccoli, N., Giachetti, R., Sorace, E. and Tarlini, M.: Free q-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group, Comm. Math. Phys. 175 (1996), 161-176.Google Scholar
- 2.Bonechi, F., Giachetti, R., del Olmo, M. A., Sorace, E. and Tarlini, M.: A new class of deformed special functions from quantum homogeneous spaces, J. Phys. A: Math. Gen., in press.Google Scholar
- 3.Brzeziński, T.: Quantum homogeneous spaces as quantum quotient spaces, J. Math. Phys. 37 (1996), 2388-2399.Google Scholar
- 4.Chari, V. and Pressley, A.: AGuide to Quantum Groups, Cambridge University Press, Cambridge,1994.Google Scholar
- 5.Ciccoli, N.: Quantum planes and quantum cylinders from Poisson homogeneous spaces, J. Phys. A: Math. Gen. 29 (1996), 1487-1495.Google Scholar
- 6.Dijkhuizen, M. S. and Koornwinder, T. H.: Quantum homogeneous spaces, duality and the quantum 2-spheres, Geom. Dedicata 52 (1994), 291-315.Google Scholar
- 7.Dijkhuizen, M. S.: Some remarks on the construction of quantum symmetric spaces, Acta Appl. Math. 44 (1996), 59-80.Google Scholar
- 8.Etingof, P. I. and Kazhdan, D.: Quantization of Poisson algebraic groups and Poisson homogeneous spaces, Preprint, October 1995.Google Scholar
- 9.Lu, J. H.: Moment maps at the quantum level, Comm. Math. Phys. 157 (1993), 389–404.Google Scholar
- 10.Lu, J. H. and Weinstein, A.: Poisson-Lie groups, dressing transformation and Bruhat decompositions, J. Differential Geom. 31 (1990), 501-526.Google Scholar
- 11.Podleś, P.: Quantum spheres, Lett. Math. Phys. 14 (1987), 193–202.Google Scholar
- 12.Podleś, P.: Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) subgroup, Comm. Math. Phys. 172 (1995), 1-20.Google Scholar
- 13.Sweedler, M.E.: Hopf Algebras, Benjamin, New York, 1969.Google Scholar
- 14.Vaisman, I.: Lectures on the Geometry of Poisson Manifolds, Progress in Math. 118, Birkhäuser-Verlag, Basel, 1994.Google Scholar
- 15.Zakrzewski, S.: Poisson homogeneous spaces, in: J. Karpacz, Z. Lukierski, Popowicz and J. Sobczik (eds), Proc. XXX Winter School on Theoretical Physics 1994, Polish Scientific Publishers PWN, Warsaw, 1995.Google Scholar
Copyright information
© Kluwer Academic Publishers 1997