Geodesic
Poisson structures associated with algebras of differential operators
Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 256-271.

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For differential operators forming an algebra of a certain class that includes algebras of higher derivatives, a Poisson structure is introduced and the first term of the Hochschild spectral sequence is calculated. 
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     title = {Poisson structures associated with algebras of differential operators},
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O. V. Lychagina. Poisson structures associated with algebras of differential operators. Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 256-271. http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a7/

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