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Associative and Lie deformations of Poisson algebras

Elisabeth Remm (2012)

Communications in Mathematics

Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.

Holomorphic Poisson Cohomology

Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)

Complex Manifolds

Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in...

Singular reduction of generalized complex manifolds.

Goldberg, Timothy E. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Tangent Dirac structures of higher order

P. M. Kouotchop Wamba, A. Ntyam, J. Wouafo Kamga (2011)

Archivum Mathematicum

Let $L$ be an almost Dirac structure on a manifold $M$ . In [2] Theodore James Courant defines the tangent lifting of $L$ on $T M$ and proves that: If $L$ is integrable then the tangent lift is also integrable. In this paper, we generalize this lifting to tangent bundle of higher order.

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Liana David (0)

Annales de l’institut Fourier