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Calculus on Poisson Manifolds
Author(s) -
Bhaskara K. H.,
Viswanath K.
Publication year - 1988
Publication title -
bulletin of the london mathematical society
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/20.1.68
Subject(s) - mathematics , covariance and contravariance of vectors , manifold (fluid mechanics) , pure mathematics , calculus (dental) , poisson distribution , poisson bracket , poisson manifold , space (punctuation) , dual (grammatical number) , algebra over a field , lie algebra , medicine , statistics , dentistry , mechanical engineering , art , linguistics , philosophy , literature , symplectic geometry , engineering
We prove the existence of a Lie bracket on the space of 1‐forms on a Poisson manifold. This gives rise to a calculus of skewsymmetric contravariant tensors dual to Cartan's calculus of forms.