dorsal/arxiv
View SchemaPoisson Algebra of Differential Forms
| Authors | Chong-Sun Chu, Pei-Ming Ho |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612031 |
| URL | https://arxiv.org/abs/q-alg/9612031 |
| DOI | 10.1142/S0217751X97002929 |
| Journal | Int.J.Mod.Phys. 12 (1997) 5573-5587 |
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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"abstract": "We give a natural definition of a Poisson Differential Algebra. Consistence\nconditions are formulated in geometrical terms. It is found that one can often\nlocally put the Poisson structure on differential calculus in a simple\ncanonical form by a coordinate transformation. This is in analogy with the\nstandard Darboux\u0027s theorem for symplectic geometry. For certain cases there\nexists a realization of the exterior derivative through a certain canonical\none-form. All the above are carried out similarly for the case of a complex\nPoisson Differential Algebra. The case of one complex dimension is treated in\ndetails and interesting features are noted. A conclusion is made in the last\nsection.",
"arxiv_id": "q-alg/9612031",
"authors": [
"Chong-Sun Chu",
"Pei-Ming Ho"
],
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"doi": "10.1142/S0217751X97002929",
"journal_ref": "Int.J.Mod.Phys. 12 (1997) 5573-5587",
"title": "Poisson Algebra of Differential Forms",
"url": "https://arxiv.org/abs/q-alg/9612031"
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