Geodesic
Splitting of function algebras on symplectic manifolds
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1982), pp. 39-41

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We derive some sufficient conditions for Lie algebras of functions on symplectic manifolds to split into the ideal of locally constant functions and an ideal isomorphic о the Lie algebra оf Hamiltonian vector fields of certain functions. A splitting of this form is produced m the case of algebras on compact manifolds. 
@article{VMUMM_1982_4_a9,
     author = {V. Hoffman},
     title = {Splitting of function algebras on symplectic manifolds},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {39--41},
     publisher = {mathdoc},
     number = {4},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_4_a9/}
}
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V. Hoffman. Splitting of function algebras on symplectic manifolds. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1982), pp. 39-41. http://geodesic.mathdoc.fr/item/VMUMM_1982_4_a9/