Geodesic
Deformations of the~antibracket with Grassmann-valued deformation parameters
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 62-77

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We consider the antibracket superalgebra realized on the space of smooth functions on $\mathbb{R}^1$ with values in the Grassmann algebra with one generator $\xi$ and consisting of elements of the form $\xi f_0(x)+f_1(x)$ with compactly supported $f_0$. Any basis of the second cohomology space with coefficients in the adjoint representation of this superalgebra consists of three odd and infinitely many even elements. We describe a large class of deformations of this superalgebra with Grassmann-valued deformation parameters. In particular, we find all deformations of this superalgebra that have exactly three odd parameters.
Mots-clés : antibracket, Poisson superalgebra.
Keywords: deformation, cohomology 
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     author = {S. E. Konstein and I. V. Tyutin},
     title = {Deformations of the~antibracket with {Grassmann-valued} deformation parameters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_1_a3/}
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S. E. Konstein; I. V. Tyutin. Deformations of the~antibracket with Grassmann-valued deformation parameters. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 62-77. http://geodesic.mathdoc.fr/item/TMF_2015_183_1_a3/