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ЖУРНАЛЫ // Lobachevskii Journal of Mathematics // Архив

Lobachevskii J. Math., 1999, том 3, страницы 201–207 (Mi ljm168)

Nnambu–Poisson structures and their foliations

K. Mikami

Department of Computer Science and Engineering, Akita University

Аннотация: Nambu–Poisson bracket is a natural generalization of Poisson bracket. A very distinguished property is its decomposability. This is investigated from the second order term of the fundamental identity (see [2] or [5]). In this paper, we shall study the first order term of the fundamental identity and get a relation with the Schouten–Nijenhuis bracket. And also we shall show that for a given Poisson structure, the top power of it gives a Nambu–Poisson structure. We shall characterize the Godbillon–Vey class of the foliation defined from a regular Nambu–Poisson tensor.

Ключевые слова: Nambu-Poisson structure/bracket/tensor, foliation, Godbillon-Vey class.

Поступило: 27.07.1999

Язык публикации: английский



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