Quantum duality principle for coisotropic subgroups and Poisson quotients
Abstract
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to produce quantizations of the dual coisotropic subgroup (in the dual formal Poisson group). By the natural link between subgroups and homogeneous spaces, we argue a quantum duality principle for Poisson homogeneous spaces which are Poisson quotients, i.e. have at least one zero-dimensional symplectic leaf. Only bare results are presented, while detailed proofs can be found in math.QA/0412465, or in the reference [3]. The last section contains new, unpublished material about examples and applications, which is not included in math.QA/0412465 (nor in its printed version).
Cite
@article{arxiv.math/0603376,
title = {Quantum duality principle for coisotropic subgroups and Poisson quotients},
author = {Nicola Ciccoli and Fabio Gavarini},
journal= {arXiv preprint arXiv:math/0603376},
year = {2011}
}
Comments
La-TeX file, 20 pages. This is a seminal version of math.QA/0412465, as reported by the second author in the conference "Contemporary Geometry and Related Topics 2005" (Belgrade, June 26-July 2, 2005); the last section contains new, unpublished material about examples and applications, *which is not included in math.QA/0412465*. This is the final version