Geodesic
Associative and Lie deformations of Poisson algebras
Communications in Mathematics, Tome 20 (2012) no. 2, pp. 117-136

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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.
Classification : 17B63, 17Dxx, 53Dxx
Keywords: Poisson algebras; deformations; operads; cohomology 
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     author = {Remm, Elisabeth},
     title = {Associative and {Lie} deformations of {Poisson} algebras},
     journal = {Communications in Mathematics},
     pages = {117--136},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2012},
     mrnumber = {3032808},
     zbl = {06165039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2012__20_2_a4/}
}
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Remm, Elisabeth. Associative and Lie deformations of Poisson algebras. Communications in Mathematics, Tome 20 (2012) no. 2, pp. 117-136. http://geodesic.mathdoc.fr/item/COMIM_2012__20_2_a4/