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A quantum duality principle for subgroups and homogeneous spaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ciccoli, Nicola Gavarini, Fabio |
| Copyright Year | 2003 |
| Abstract | We develop a quantum duality principle for subgroups of a Poisson group and its dual, in two formulations: namely, in the first one we provide functorial recipes to produce quantum coisotropic subgroups in the dual Poisson group out of any quantum subgroup (in a tautological sense) of the initial Poisson group, while in the second one similar recipes are given only starting from coisotropic subgroups. In both cases this yields a Galois-type correspondence, where a quantum coisotropic subgroup is mapped to its complementary dual; moreover, in the first formulation quantum coisotropic subgroups are characterized as being the fixed points in this Galois’ reciprocity. By the natural link between quantum subgroups and quantum homogeneous spaces then we argue a quantum duality principle for homogeneous spaces too, where quantum coisotropic spaces are the fixed elements in a Galois’ reciprocity. As an application, we provide an explicit quantization of the homogeneous SLn(C) ∗–space of Stokes matrices, with the Poisson structure given by Dubrovin and Ugaglia. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0312289v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0312289v2.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0312289v4.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
