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

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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 2, Pages 41–51
DOI: https://doi.org/10.4213/faa147 (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

Full-text PDF (172 kB) Citations (7)

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

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.

Received: 29.05.2002

English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 2, Pages 114–122
DOI: https://doi.org/10.1023/A:1024404922951

Bibliographic databases:

Document Type: Article

UDC: 514.75

Language: Russian

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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This publication is cited in the following 7 articles:

S. A. Shashkov, “Commutative homogeneous spaces with one-dimensional stabilizer”, Izv. Math., 76:4 (2012), 820–839
Yakimova O., “Principal Gelfand pairs”, Transform. Groups, 11:2 (2006), 305–335
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
L. G. Rybnikov, “Weakly commutative homogeneous spaces with reductive stabilizer”, Russian Math. Surveys, 59:4 (2004), 798–799
Yakimova O., “Saturated commutative spaces of Heisenberg type”, Acta Appl. Math., 81:1 (2004), 339–345
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
O. S. Yakimova, “On the classification of Gel'fand pairs”, Russian Math. Surveys, 58:3 (2003), 619–621

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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