ar X iv : m at h / 99 02 12 8 v 2 [ m at h . D G ] 7 M ar 1 99 9 Remarks on Nambu - Poisson , and Nambu - Jacobi brackets
نویسندگان
چکیده
We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.
منابع مشابه
m at h . D G ] 1 5 A pr 1 99 9 Remarks on Nambu - Poisson , and Nambu - Jacobi brackets
We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.
متن کاملar X iv : h ep - t h / 95 07 12 5 v 1 2 4 Ju l 1 99 5 Aspects of Classical and Quantum Nambu Mechanics
We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations. Mathematics Subject Classification (1991) 70H99, 58F07
متن کامل. D G ] 2 3 Fe b 19 99 Remarks on Nambu - Poisson , and Nambu - Jacobi brackets
We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.
متن کاملar X iv : h ep - t h / 97 03 01 9 v 1 3 M ar 1 99 7 DAMTP 97 – 12 On the generalizations of Poisson structures
The characterization of the Nambu-Poisson n-tensors as a subfamily of the Generalized-Poisson ones recently introduced is discussed. The homol-ogy and cohomology complexes associated with both higher order Poisson structures are compared, and some physical considerations are made.
متن کاملar X iv : m at h - ph / 9 80 70 18 v 1 1 7 Ju l 1 99 8 Volume preserving multidimensional integrable systems and Nambu - Poisson Geometry
In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu-Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. Recently Takasaki-Takebe provided the twistor construction of dispersionless KP and dToda type equations by us...
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تاریخ انتشار 1998