Geodesic
Deformations of the nondegenerate constant Poisson bracket and
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 109-116
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider {(}anti-{\rm)}Poisson superalgebras with a constant nondegenerate {\rm(}anti{\rm)}bracket realized on smooth Grassmann-valued functions with compact supports in $\mathbb{R}^n$ and find the deformations of these superalgebras and their central extensions.
Mots-clés : Poisson superalgebra, anti-Poisson superalgebra, quantization.
Keywords: superbracket deformation, superalgebra cohomology 
@article{TMF_2008_155_1_a8,
     author = {S. E. Konstein and I. V. Tyutin},
     title = {Deformations of the nondegenerate constant {Poisson} bracket and},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {109--116},
     year = {2008},
     volume = {155},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a8/}
}
TY  - JOUR
AU  - S. E. Konstein
AU  - I. V. Tyutin
TI  - Deformations of the nondegenerate constant Poisson bracket and
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 109
EP  - 116
VL  - 155
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a8/
LA  - ru
ID  - TMF_2008_155_1_a8
ER  - 
%0 Journal Article
%A S. E. Konstein
%A I. V. Tyutin
%T Deformations of the nondegenerate constant Poisson bracket and
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 109-116
%V 155
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a8/
%G ru
%F TMF_2008_155_1_a8
S. E. Konstein; I. V. Tyutin. Deformations of the nondegenerate constant Poisson bracket and. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 109-116. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a8/

[1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovich, D. Sternheimer, Ann. Phys., 111:1 (1978), 61–110 | DOI | MR | Zbl

[2] M. V. Karasev, V. P. Maslov, Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991 | MR | MR | Zbl

[3] B. Fedosov, Deformation Quantization and Index Theory, Akademie, Berlin, 1996 | MR | Zbl

[4] M. Kontsevich, Lett. Math. Phys., 66:3 (2003), 157–216 ; arXiv: q-alg/9709040 | DOI | MR | Zbl

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

[6] I. V. Tyutin, TMF, 128:3 (2001), 515–539 | DOI | MR | Zbl

[7] V. V. Zharinov, TMF, 136:2 (2003), 179–196 | DOI | MR | Zbl

[8] S. E. Konshtein, A. G. Smirnov, I. V. Tyutin, TMF, 148:2 (2006), 163–178 ; arXiv: hep-th/0401023 | DOI | MR

[9] S. E. Konstein, I. V. Tyutin, General form of the deformation of Poisson superbracket on $(2,n)$-dimensional superspace, , predst. v TMF arXiv: hep-th/0610308 | MR

[10] S. E. Konstein, I. V. Tyutin, Deformations of the central extension of the Poisson superalgebra, , predst. v TMF arXiv: hep-th/0501027 | MR

[11] S. E. Konstein, I. V. Tyutin, Deformations of the antibracket, arXiv: hep-th/0512313

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

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

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

[15] I. A. Batalin, G. A. Vilkovisky, Phys. Lett. B, 120:1–3 (1983), 166–170 | DOI

[16] I. A. Batalin, G. A. Vilkovisky, J. Math. Phys., 26:1 (1985), 172–184 | DOI | MR

[17] J. Gomis, J. Paris, S. Samuel, Phys. Rep., 259:1–2 (1995), 1–145 ; arXiv: hep-th/9412228 | DOI | MR

[18] D. M. Gitman, I. V. Tyutin, Kanonicheskoe kvantovanie polei so svyazyami, Nauka, M., 1986 | MR | MR | Zbl

[19] M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, University Press, Princeton, NJ, 1992 | MR | Zbl

[20] S. E. Konstein, I. V. Tyutin, Cohomology of antiPoisson superalgebra, arXiv: hep-th/0512300