SEVERAL COHOMOLOGY ALGEBRAS CONNECTED WITH THE POISSON STRUCTURE

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Abstract

ABSTRACT

The structure of a Lie superalgebra is defined on the space of multiderivations of a commutative algebra. This structure is used to define some cohomology algebra of Poisson structure. It is shown that when a commutative algebra is an algebra of C∞-functions on the C∞-manifold, the cohomology algebra of Poisson structure is isomorphic to an algebra of vertical cohomologies of the foliation corresponding to the Poisson structure.

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