Geodesic
On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 41-51

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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.
Mots-clés : Lie group, Poisson bracket
Keywords: Lie algebra, universal enveloping algebra, homogeneous space, (weakly) commutative space, symplectic manifold, momentum map. 
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     author = {L. G. Rybnikov},
     title = {On the {Commutativity} of {Weakly} {Commutative} {Riemannian} {Homogeneous} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a4/}
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L. G. Rybnikov. On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 41-51. http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a4/