Quantization of Co-Isotropic Subgroups

Letters in Mathematical Physics

Volumn 42, Issue 2, 1997, Pages 123-138

  Ciccoli, Nicola ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

One sided ideals; Poisson homogeneous spaces; Poisson subgroups; Quantum homogeneous spaces; Quantum quotients; Quantum subgroups

Indexed keywords

EID: 0001088055     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007352218739     Document Type: Article

References (15)

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.
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.
3. Brzeziński, T.: Quantum homogeneous spaces as quantum quotient spaces, J. Math. Phys. 37 (1996), 2388-2399.
4. Chari, V. and Pressley, A.: A Guide to Quantum Groups, Cambridge University Press, Cambridge, 1994.
5. Ciccoli, N.: Quantum planes and quantum cylinders from Poisson homogeneous spaces, J. Phys. A: Math. Gen. 29 (1996), 1487-1495.
6. Dijkhuizen, M. S. and Koornwinder, T. H.: Quantum homogeneous spaces, duality and the quantum 2-spheres, Geom. Dedicata 52 (1994), 291-315.
7. Dijkhuizen, M. S.: Some remarks on the construction of quantum symmetric spaces, Acta Appl. Math. 44 (1996), 59-80.
8. Etingof, P. I. and Kazhdan, D.: Quantization of Poisson algebraic groups and Poisson homogeneous spaces, Preprint, October 1995.
9. Lu, J. H.: Moment maps at the quantum level, Comm. Math. Phys. 157 (1993), 389-404.
10. Lu, J. H. and Weinstein, A.: Poisson-Lie groups, dressing transformation and Bruhat decompositions, J. Differential Geom. 31 (1990), 501-526.
11. Podleś, P.: Quantum spheres, Lett. Math. Phys. 14 (1987), 193-202.
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.
13. Sweedler, M.E.: Hopf Algebras, Benjamin, New York, 1969.
14. Vaisman, I.: Lectures on the Geometry of Poisson Manifolds, Progress in Math. 118, Birkhäuser-Verlag, Basel, 1994.
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.