Displaying similar documents to “Divergence operators and odd Poisson brackets”

From Poisson algebras to Gerstenhaber algebras

Yvette Kosmann-Schwarzbach (1996)

Annales de l'institut Fourier

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Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie...

Hochschild cohomology and quantization of Poisson structures

Grabowski, Janusz

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It is well-known that the question of existence of a star product on a Poisson manifold N is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures P of the following type P = X ∧ Y with [ X , Y ] = u X + v Y , for some u , v ∈ C ∞ ( N , ℝ ) .