Several Cohomology Algebras Connected with the Poisson Structure |
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| Authors: | Giunashvili Z. |
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| Affiliation: | (1) Georgian Academy of Sciences, A. Razmadze Mathematical Institute, 1, Aleksidze St., Tbilisi, 390093, Georgia |
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| 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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| Keywords: | Lie superalgebra Poisson structure vertical cohomology cohomology of Poisson structure |
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