Geodesic
Non-decomposable Nambu brackets
Archivum mathematicum, Tome 51 (2015) no. 4, pp. 211-232
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It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.
It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.
DOI : 10.5817/AM2015-4-211
Classification : 53D17, 53D99, 58A10, 70G10, 70G45, 70H50
Keywords: Nambu bracket; Darboux Theorem; Moser trick; multisymplectic; presymplectic; Weinstein splitting principle 
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Bering, Klaus. Non-decomposable Nambu brackets. Archivum mathematicum, Tome 51 (2015) no. 4, pp. 211-232. doi: 10.5817/AM2015-4-211

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