Extending our reduction construction in (S. Hu, Hamiltonian symmetries and reduction in generalized geometry, Houston J. Math., to appear, math.DG/0509060, 2005.) to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) T-duality with H-fluxes for principle bundles naturally arise as reductions of factorizable Poisson Lie group actions. In particular, the groups involved may be non-abelian.
Hu, Shengda, "Reduction and Duality in Generalized Geometry" (2007). Mathematics Faculty Publications. 27.