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On one class of exact Poisson structures. (English) Zbl 1060.53502
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:
53D17Poisson manifolds; Poisson groupoids and algebroids
17B63Poisson algebras
17B81Applications of Lie algebras to physics