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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:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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