Poisson Algebra of Differential Forms

Details Poisson Algebra of Differential Forms Poisson Algebra of Differential Forms

1996-12-24

arxiv.org/abs/q-alg/9612031v2

Int.J.Mod.Phys. 12 (1997) 5573-5587

Mathematics

Quantum Algebra

Latex, 14 pages, no figure, typos corrected, references added

Scientific paper

10.1142/S0217751X97002929

We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form by a coordinate transformation. This is in analogy with the standard Darboux's theorem for symplectic geometry. For certain cases there exists a realization of the exterior derivative through a certain canonical one-form. All the above are carried out similarly for the case of a complex Poisson Differential Algebra. The case of one complex dimension is treated in details and interesting features are noted. A conclusion is made in the last section.

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