# Non-decomposable Nambu brackets

## Klaus Bering

Address: Institute for Theoretical Physics and Astrophysics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: bering@physics.muni.cz

Abstract: 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.

AMSclassification: primary 53D17; secondary 53D99, 58A10, 70G10, 70G45, 70H50.

Keywords: Nambu bracket, Darboux Theorem, Moser trick, multisymplectic, presymplectic, Weinstein splitting principle.

DOI: 10.5817/AM2015-4-211