57 research outputs found
The coisotropic subgroup structure of SL_q(2,R)
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 family of quantum coisotropic subgroups whose coalgebra can not
be extended to an Hopf algebra. We explicitly describe the quantum homogeneous
spaces and their double cosets.Comment: LaTex2e, 10pg, no figure
Noncommutative Instantons on the 4-Sphere from Quantum Groups
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 structure of U(4) shows that the diagonal SU(2) must
be conjugated to be properly quantized. The quantum coisotropic subgroup we
obtain is the standard SU_q(2); it determines a new deformation of the 4-sphere
Sigma^4_q as the algebra of coinvariants in S_q^7. We show that the quantum
vector bundle associated to the fundamental corepresentation of SU_q(2) is
finitely generated and projective and we compute the explicit projector. We
give the unitary representations of Sigma^4_q, we define two 0-summable
Fredholm modules and we compute the Chern-Connes pairing between the projector
and their characters. It comes out that even the zero class in cyclic homology
is non trivial.Comment: 16 pages, LaTeX; revised versio
Bijectivity of the canonical map for the noncommutative instanton bundle
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 versio
Quantum planes and quantum cylinders from Poisson homogeneous spaces
Quantum planes and a new quantum cylinder are obtained as quantization of
Poisson homogeneous spaces of two different Poisson structures on classical
Euclidean group E(2).Comment: 13 pages, plain Tex, no figure
Quantum even spheres Sigma_q^2n from Poisson double suspension
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 Poisson double suspension of the standard Podle's
two-sphere. The Poisson spheres that we get have the same symplectic foliation
consisting of a degenerate point and a symplectic plane and, after
quantization, have the same C^*-algebraic completion. We investigate their
K-homology and K-theory by introducing Fredholm modules and projectors.Comment: 13 pages; LaTeX 2
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