Zobrazeno 1 - 10
of 193
pro vyhledávání: '"Ciccoli, N."'
We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singula
Externí odkaz:
http://arxiv.org/abs/1306.4175
Publikováno v:
Journal of Geometry and Physics Volume: 62 Issue: 8 Pages: 1851-1865 (2012)
We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a
Externí odkaz:
http://arxiv.org/abs/1004.3163
Publikováno v:
Journal of Noncommutative Geometry 2 (2008), 449-496
We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generalized flag varieties. Using this construction, we extend the quantum dual
Externí odkaz:
http://arxiv.org/abs/0801.4033
Publikováno v:
J.Geom.Phys. 58 (2008) 1519-1529
We study a reduction procedure for describing the symplectic groupoid of a Poisson homogeneous space obtained by quotient of a coisotropic subgroup. We perform it as a reduction of the Lu-Weinstein symplectic groupoid integrating Poisson Lie groups,
Externí odkaz:
http://arxiv.org/abs/0711.0361
Autor:
Ciccoli, N., Sheu, A. J. -L.
The purpose of this paper is to study covariant Poisson structures on the complex Grassmannian obtained as quotients by coisotropic subgroups of the standard Poisson--Lie SU(n). Properties of Poisson quotients allow to describe Poisson embeddings gen
Externí odkaz:
http://arxiv.org/abs/math/0503218
Publikováno v:
Journal of Geometry and Physics 51 (2004)71-81
It is shown that the quantum instanton bundle introduced in Commun. Math. Phys. 226, 419-432 (2002) has a bijective canonical map and is, therefore, a coalgebra Galois extension.
Comment: Latex, 12 pages. Published version
Comment: Latex, 12 pages. Published version
Externí odkaz:
http://arxiv.org/abs/math/0306114
Publikováno v:
Commun.Math.Phys.243:449-459,2003
We define even dimensional quantum spheres Sigma_q^2n that generalize to higher dimension the standard quantum two-sphere of Podle's and the four-sphere Sigma_q^4 obtained in the quantization of the Hopf bundle. The construction relies on an iterated
Externí odkaz:
http://arxiv.org/abs/math/0211462
Publikováno v:
J. Nonlinear Math. Phys. 9-suppl 2 (2002) pp. 24-35
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.
Externí odkaz:
http://arxiv.org/abs/nlin/0205064
Publikováno v:
Commun.Math.Phys.226:419-432,2002
We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle S^7 --> S^4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson--Lie
Externí odkaz:
http://arxiv.org/abs/math/0012236
Publikováno v:
J.Geom.Phys.37:190-200,2001
We study the coisotropic subgroup structure of standard SL_q(2,R) and the corresponding embeddable quantum homogeneous spaces. While the subgroups S^1 and R_+ survive undeformed in the quantization as coalgebras, we show that R is deformed to a famil
Externí odkaz:
http://arxiv.org/abs/math/9907048