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Poisson brackets with divergence terms in field theories: Three examples. (English) Zbl 0988.37099
McCleary, John (ed.), Higher homotopy structures in topology and mathematical physics. Proceedings of an international conference, June 13-15, 1996, Poughkeepsie, NY, USA, to honor the 60th birthday of Jim Stasheff. Providence, RI: American Mathematical Society. Contemp. Math. 227, 67-78 (1999).
The author considers three examples of trilinear form which appears as a result calculating Poisson brackets of two functionals defined up to divergence terms. Two examples are related to the simplest one-dimensional case and the third one is two-dimensional. They naturally appear in the Hamiltonian theory of 2D inviscid, incompressible fluids.
For the entire collection see [Zbl 0904.00041].

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
53D17 Poisson manifolds; Poisson groupoids and algebroids
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
81T70 Quantization in field theory; cohomological methods