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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 2, Pages 41–51 (Mi faa147)  

This article is cited in 7 scientific papers (total in 7 papers)

On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces

L. G. Rybnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A Riemannian homogeneous space $X=G/H$ is said to be commutative if the algebra of $G$-invariant differential operators on $X$ is commutative and weakly commutative if the associated Poisson algebra is commutative. Clearly, the commutativity of $X$ implies its weak commutativity. The converse implication is proved in this paper.

Keywords: Lie group, Lie algebra, universal enveloping algebra, homogeneous space, (weakly) commutative space, symplectic manifold, Poisson bracket, momentum map

DOI: https://doi.org/10.4213/faa147

Full text: PDF file (172 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:2, 114–122

Bibliographic databases:

UDC: 514.75
Received: 29.05.2002

Citation: L. G. Rybnikov, “On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 41–51; Funct. Anal. Appl., 37:2 (2003), 114–122

Citation in format AMSBIB
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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. O. S. Yakimova, “On the classification of Gel'fand pairs”, Russian Math. Surveys, 58:3 (2003), 619–621  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. L. G. Rybnikov, “Weakly commutative homogeneous spaces with reductive stabilizer”, Russian Math. Surveys, 59:4 (2004), 798–799  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Yakimova O., “Saturated commutative spaces of Heisenberg type”, Acta Appl. Math., 81:1 (2004), 339–345  crossref  mathscinet  zmath  isi  scopus
    4. Rybnikov L.G., “Structure of the center of the algebra of invariant differential operators on certain Riemannian homogeneous spaces”, Transform. Groups, 9:4 (2004), 381–397  crossref  mathscinet  zmath  isi
    5. L. G. Rybnikov, “Centralizers of certain quadratic elements in Poisson–Lie algebras and the method of translation of invariants”, Russian Math. Surveys, 60:2 (2005), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Yakimova O., “Principal Gelfand pairs”, Transform. Groups, 11:2 (2006), 305–335  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. A. Shashkov, “Commutative homogeneous spaces with one-dimensional stabilizer”, Izv. Math., 76:4 (2012), 820–839  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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