Geodesic
General Form of the $*$-Commutator on the Grassmann Algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 515-539

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The general form of the $*$-commutator on the Grassmann algebra treated as a deformation of the conventional Poisson bracket is investigated. It is shown that in addition to the Moyal $*$-commutator, there exist other deformations of the Poisson bracket on the Grassman algebra (one additional deformation for even and odd $n$, where $n$ is the number of the Grassmann algebra generators) that are not reducible to the Moyal $*$-commutator by a similarity transformation. 
@article{TMF_2001_128_3_a13,
     author = {I. V. Tyutin},
     title = {General {Form} of the $*${-Commutator} on the {Grassmann} {Algebra}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {515--539},
     publisher = {mathdoc},
     volume = {128},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a13/}
}
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I. V. Tyutin. General Form of the $*$-Commutator on the Grassmann Algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 515-539. http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a13/