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arXiv · q-alg/9612031

Poisson Algebra of Differential Forms

Chong-Sun Chu·Pei-Ming Ho
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Abstract

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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BibTeXRIS

Chong-Sun Chu, Pei-Ming Ho. 1997-01-31. Poisson Algebra of Differential Forms. https://doi.org/10.1142/s0217751x97002929

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