Geodesic
Cohomology of the Poisson Superalgebra on Spaces of Superdimension $(2,n_-)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 3, pp. 291-320

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Under certain assumptions about the continuity of cochains, we study the cohomology spaces of a Poisson superalgebra realized on the space of smooth Grassmann-valued functions with compact support in $\mathbb{R}^2$. We find the zeroth, first, and second cohomology spaces in the adjoint representation in the case of a constant nondegenerate Poisson superbracket.
Keywords: Grassmann algebra, cohomology, deformation, $*$-commutator
Mots-clés : Poisson superalgebra, quantization. 
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     author = {S. E. Konstein and I. V. Tyutin},
     title = {Cohomology of the {Poisson} {Superalgebra} on {Spaces} of {Superdimension} $(2,n_-)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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S. E. Konstein; I. V. Tyutin. Cohomology of the Poisson Superalgebra on Spaces of Superdimension $(2,n_-)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 3, pp. 291-320. http://geodesic.mathdoc.fr/item/TMF_2005_145_3_a0/