A global quantum duality principle for subgroups and homogeneous spaces
Documenta mathematica, Tome 19 (2014), pp. 333-380
For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras Fq[G] or Uq(g) over C[q,q−1]. Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on g: correspondingly, one has dual Poisson groups G∗ and a dual Lie bialgebra g∗. In this context, we introduce suitable notions of quantum subgroup and, correspondingly, of quantum homogeneous space, in three versions: weak, proper and strict (also called flat in the literature). The last two notions only apply to those subgroups which are coisotropic, and those homogeneous spaces which are Poisson quotients; the first one instead has no restrictions whatsoever.
Classification :
17B37, 20G42, 58B32, 81R50
Mots-clés : quantum groups, Poisson homogeneous spaces, coisotropic subgroups
Mots-clés : quantum groups, Poisson homogeneous spaces, coisotropic subgroups
@article{10_4171_dm_449,
author = {Nicola Ciccoli and Fabio Gavarini},
title = {A global quantum duality principle for subgroups and homogeneous spaces},
journal = {Documenta mathematica},
pages = {333--380},
year = {2014},
volume = {19},
doi = {10.4171/dm/449},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/449/}
}
Nicola Ciccoli; Fabio Gavarini. A global quantum duality principle for subgroups and homogeneous spaces. Documenta mathematica, Tome 19 (2014), pp. 333-380. doi: 10.4171/dm/449
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