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Graded Poisson structures on the algebra of differential forms
J. V. BeltranJ. V. BeltranJuan MonterdeJuan Monterdesubject
Mathematics::Commutative AlgebraGeneral MathematicsMathematics::Rings and AlgebrasMathematical analysisGraded ringGraded Lie algebraFrölicher–Nijenhuis bracketAlgebraPoisson bracketDifferential graded algebraExterior derivativeMathematics::Symplectic GeometryFirst class constraintMathematicsPoisson algebradescription
We study the graded Poisson structures defined on Ω(M), the graded algebra of differential forms on a smooth manifoldM, such that the exterior derivative is a Poisson derivation. We show that they are the odd Poisson structures previously studied by Koszul, that arise from Poisson structures onM. Analogously, we characterize all the graded symplectic forms on ΩM) for which the exterior derivative is a Hamiltomian graded vector field. Finally, we determine the topological obstructions to the possibility of obtaining all odd symplectic forms with this property as the image by the pullback of an automorphism of Ω(M) of a graded symplectic form of degree 1 with respect to which the exterior derivative is a Hamiltonian graded vector field.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-12-01 | Commentarii Mathematici Helvetici |