%0 Generic %1 citeulike:5071 %A Ciccoli, Nicola %A Gavarini, Fabio %D 2004 %K qm %T A quantum duality principle for coisotropic subgroups and Poisson quotients %U http://arxiv.org/abs/math.QA/0412465 %X 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. As an application, we provide an explicit quantization of the homogeneous SL(n)^*-space of Stokes matrices, with the Poisson structure given by Dubrovin and Ugaglia. A "global version" of these results were previously posted as <A HREF="/abs/math.QA/0312289">math.QA/0312289</A>, which is actually under review (there, non-formal quantizations - via ordinary Hopf algebras over the ring of Laurent polynomials - were considered of global - rather than local - Poisson groups, homogeneous spaces and subgroups).

@misc{citeulike:5071, 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. As an application, we provide an explicit quantization of the homogeneous SL(n)^*-space of Stokes matrices, with the Poisson structure given by Dubrovin and Ugaglia. A "global version" of these results were previously posted as <A HREF="/abs/math.QA/0312289">math.QA/0312289</A>, which is actually under review (there, non-formal quantizations - via ordinary Hopf algebras over the ring of Laurent polynomials - were considered of global - rather than local - Poisson groups, homogeneous spaces and subgroups).}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Ciccoli, Nicola and Gavarini, Fabio}, biburl = {https://www.bibsonomy.org/bibtex/257717f5583cd23f51a517f3e0c8fcd2f/a_olympia}, citeulike-article-id = {5071}, description = {citeulike}, eprint = {math.QA/0412465}, interhash = {c07d364da8ab30828d6c7b44ab7c2b33}, intrahash = {57717f5583cd23f51a517f3e0c8fcd2f}, keywords = {qm}, month = {December}, timestamp = {2007-08-18T13:23:02.000+0200}, title = {A quantum duality principle for coisotropic subgroups and Poisson quotients}, url = {http://arxiv.org/abs/math.QA/0412465}, year = 2004 }