m at h . D G ] 1 5 A pr 1 99 9 Remarks on Nambu - Poisson , and Nambu - Jacobi brackets
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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
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
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 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.
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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
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The Poisson, contact and Nambu brackets define algebraic structures on C∞(M) satisfying the Jacobi identity or its generalization. The automorphism groups of these brackets are the symplectic, contact and volume preserving diffeomorphism groups. We introduce a modification of the Nambu bracket, which define an evolution equation generating the whole diffeomorphism group. The relation between th...
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تاریخ انتشار 1998