Geodesic
Deformations of the antibracket with Grassmann-valued deformation parameters
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 62-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] S. E. Konstein, I. V. Tyutin, The deformations of antibracket with even and odd deformation parameters, arXiv: 1011.5807

[2] S. E. Konstein, I. V. Tyutin, J. Math. Phys., 49:7 (2008), 072103, 41 pp. | DOI | MR | Zbl

[3] S. E. Konstein, I. V. Tyutin, The deformations of antibracket with even and odd deformation parameters, defined on the space $DE_1$, arXiv: 1112.1686

[4] S. E. Konshtein, A. G. Smirnov, I. V. Tyutin, TMF, 143:2 (2005), 163–194, arXiv: hep-th/0312109 | DOI | MR

[5] I. I. Bernshtein, D. A. Leites, V. N. Shander, Seminar po supersimmetriyam, v. 1, Algebra i analiz: osnovnye fakty, MTsNMO, M., 2011

[6] F. A. Berezin, Vvedenie v superanaliz, MTsNMO, M., 2013

[7] M. Scheunert, R. B. Zhang, J. Math. Phys., 39:9 (1998), 5024–5061, arXiv: q-alg/9701037 | DOI | MR | Zbl

[8] M. Gerstenhaber, Ann. Math. (2), 79:1 (1964), 59–103 ; 99:2 (1974), 257–276 | DOI | MR | Zbl | DOI | MR | Zbl

[9] D. A. Leites, I. M. Schepochkina, TMF, 126:3 (2001), 339–369 | DOI | MR | Zbl

[10] M. Scheunert, J. Math. Phys., 20:4 (1979), 712–720 | DOI | MR | Zbl

[11] T. Covolo, J.-P. Michel, Determinants over graded-commutative algebras, a categorical viewpoint, arXiv: 1403.7474