Poisson algebra of differential forms
Journal
International Journal of Modern Physics
Journal Volume
12
Pages
5573-5587
Date Issued
1997-01
Author(s)
Abstract
We give a natural definition of a Poisson differential algebra. Consistency conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on the differential calculus in a simple canonical form by a coordinate trans-formation. 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 detail and interesting features are noted. Conclusions are made in the last section.
Type
journal article