Geodesic
General form of the deformation of the Poisson superbracket
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 163-178

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All continuous formal deformations of the Poisson algebra realized on Grassmann-valued compactly supported smooth functions on $\mathbb R^{2n}$ with $2n\ge4$ are found up to an equivalence transformation. We show that in the algebras considered, there exist additional deformations that differ from the Moyal bracket.
Keywords: Grassmann algebra, central extension, $*$-commutator, deformation
Mots-clés : Poisson superalgebra, cohomologies, quantization. 
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     author = {S. E. Konstein and A. G. Smirnov and I. V. Tyutin},
     title = {General form of the deformation of the {Poisson} superbracket},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a0/}
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S. E. Konstein; A. G. Smirnov; I. V. Tyutin. General form of the deformation of the Poisson superbracket. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 163-178. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a0/