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.
Global quantum duality principle for coisotropic subgroups and Poisson quotients
CICCOLI, Nicola;
2014
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
