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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 274–289 (Mi jmag497)  

This article is cited in 6 scientific papers (total in 6 papers)

The classification of Poisson homogeneous spaces of compact Poisson–Lie group

E. A. Karolinsky

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: 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.

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Received: 24.09.1996

Citation: E. A. Karolinsky, “The classification of Poisson homogeneous spaces of compact Poisson–Lie group”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 274–289

Citation in format AMSBIB
\Bibitem{Kar96}
\by E.~A.~Karolinsky
\paper The classification of Poisson homogeneous spaces of compact Poisson--Lie group
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 3/4
\pages 274--289
\mathnet{http://mi.mathnet.ru/jmag497}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Weinstein A., “Poisson Geometry”, Differ. Geom. Appl., 9:1-2 (1998), 213–238  crossref  mathscinet  zmath  isi
    2. Evens S., Lu J., “Poisson Harmonic Forms, Kostant Harmonic Forms, and the S-1-Equivariant Cohomology of K/T”, Adv. Math., 142:2 (1999), 171–220  crossref  mathscinet  zmath  isi
    3. Lu J., “Classical Dynamical R-Matrices and Homogeneous Poisson Structures on G/H and K/T”, Commun. Math. Phys., 212:2 (2000), 337–370  crossref  mathscinet  zmath  isi
    4. Evens S., Lu J., “On the Variety of Lagrangian Subalgebras, I”, Ann. Sci. Ec. Norm. Super., 34:5 (2001), 631–668  crossref  mathscinet  zmath  isi
    5. Karolinsky E., Stolin A., “Classical Dynamical R-Matrices, Poisson Homogeneous Spaces, and Lagrangian Subalgebras”, Lett. Math. Phys., 60:3 (2002), 257–274  crossref  mathscinet  zmath  isi
    6. Neshveyev S., Tuset L., “Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers”, Commun. Math. Phys., 312:1 (2012), 223–250  crossref  mathscinet  zmath  isi  elib
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