Divergence Operators and Odd Poisson Brackets
نویسنده
چکیده
We study various generating operators of a given odd Poisson bracket on a supermanifold. They arise as the operators that map a function to the divergence of the associated hamiltonian derivation, where divergences of derivations can be defined either in terms of berezinian volumes or of graded connections. Examples include generators of the Schouten bracket of multivectors on a manifold (the supermanifold being the cotangent bundle where the coordinates in the fibres are odd), generators of the Koszul-Schouten bracket of forms on a Poisson manifold (the supermanifold being the tangent bundle, with odd coordinates on the fibres) and the “odd laplacian”, ∆, of Batalin-Vilkovisky quantization.
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