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Zbl 1060.53502
Khimshiashvili, G.
On one class of exact Poisson structures. (English)
[J] Proc. A. Razmadze Math. Inst. 119, 111-120 (1999). ISSN 1512-0007

Summary: We introduce a class of Poisson structures defined by a simple explicit formula and establish basic properties of these structures. It is shown that this construction gives non-trivial examples of Poisson structures on affine algebraic varieties. For such structures on hypersurfaces in $C^3$, their zero-dimensional Poisson homology is computed in terms of Milnor numbers of Casimir polynomials. Some generalizations and open problems are also discussed.

MSC 2000:: *53D17 Poisson manifolds
17B63 Poisson algebras
17B81 Applications of Lie algebras to physics

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Zentralblatt MATH Berlin [Germany]