Multi-Derivations and Kähler Forms
The algebraic structure of the space of differential forms on a manifold is well-known; the algebraic structure on the space of multi-vector fields may be less well-known. We present both here, together with the algebraic counterpart of these spaces, which are respectively the spaces of Kähler forms and of skew-symmetric multi-derivations of an algebra. It leads to the Gerstenhaber structure on the space of multi-vector fields of a given manifold (or multi-derivations of a given algebra), a space in which the Poisson structure lives and which acts on the space of differential forms on the manifold (Kähler forms of the algebra), via the generalized Lie derivative.
KeywordsDifferential Form Poisson Bracket Poisson Structure Wedge Product Grade Vector Space
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