On Nambu–Poisson Manifolds
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説明
+ {g1, {f1, . . . , fn−1, g2}, g3, . . . , gn} + · · ·+ {g1, . . . , gn−1, {f1, . . . , fn−1, gn}} for all f1, . . . , fn−1, g1, . . . , gn ∈ C∞(M). We should note that (f1, . . . , fn−1) acts on {g1, . . . , gn} as a derivation. If n = 2, we have usual Poisson manifolds. But if n ≥ 3, there appear some aspects which are different from the case of usual Poisson manifolds. More precisely, Nambu–Poisson structure should be more rigid than usual Poisson structure. (For example, see Theorem 5.5.) P. Gautheron [3] also proved the same result as ours in a completely different way. Using the Fundamental Identity, we know that the flow of the equation of motion induces an automorphism of a Nambu–Poisson bracket.
収録刊行物
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- Reviews in Mathematical Physics
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Reviews in Mathematical Physics 10 499-510, 1998-05-01
World Scientific Pub Co Pte Lt
