Poisson Algebra of Differential Forms

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.

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

References in corpus (2)

• Differential Calculus on Quantum Spaces and Quantum Groups
• The Braided Quantum 2-Sphere

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