Geodesic
The classification of Poisson homogeneous spaces of compact Poisson--Lie group
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996), pp. 274-289.

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The classification of all Poisson homogeneous spaces with connected stabilizers of compact Poisson–Lie group $K$ (equipped with the standard $r$-matrix Poisson structure) is given. The connected closed subgroups $H\subset K$ such that $K/H$ admits a structure of Poisson homogeneous $K$-space are listed. The geometric interpretation of some of Poisson homogeneous $K$-spaces is also given. 
@article{JMAG_1996_3_a4,
     author = {E. A. Karolinsky},
     title = {The classification of {Poisson} homogeneous spaces of compact {Poisson--Lie} group},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {274--289},
     publisher = {mathdoc},
     volume = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_a4/}
}
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E. A. Karolinsky. The classification of Poisson homogeneous spaces of compact Poisson--Lie group. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996), pp. 274-289. http://geodesic.mathdoc.fr/item/JMAG_1996_3_a4/