Geodesic
Cohomologies of the Poisson superalgebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 2, pp. 163-194 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $\mathbb{R}^{2n}$ are investigated under suitable continuity restrictions on the cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket or arbitrary $n>0$. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary $n>1$.
Keywords: Grassmann algebra, deformation, $*$-commutator
Mots-clés : Poisson superalgebra, cohomologies, quantization. 
@article{TMF_2005_143_2_a0,
     author = {S. E. Konstein and A. G. Smirnov and I. V. Tyutin},
     title = {Cohomologies of the {Poisson} superalgebra},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--194},
     year = {2005},
     volume = {143},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_2_a0/}
}
TY  - JOUR
AU  - S. E. Konstein
AU  - A. G. Smirnov
AU  - I. V. Tyutin
TI  - Cohomologies of the Poisson superalgebra
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 163
EP  - 194
VL  - 143
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_143_2_a0/
LA  - ru
ID  - TMF_2005_143_2_a0
ER  - 
%0 Journal Article
%A S. E. Konstein
%A A. G. Smirnov
%A I. V. Tyutin
%T Cohomologies of the Poisson superalgebra
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 163-194
%V 143
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2005_143_2_a0/
%G ru
%F TMF_2005_143_2_a0
S. E. Konstein; A. G. Smirnov; I. V. Tyutin. Cohomologies of the Poisson superalgebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 2, pp. 163-194. http://geodesic.mathdoc.fr/item/TMF_2005_143_2_a0/

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

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

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

[4] M. Kontsevich, Lett. Math. Phys., 66 (2003), 157 ; E-print q-alg/9709040 | DOI | MR | Zbl

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

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

[7] I. V. Tyutin, TMF, 127:2 (2001), 253 | DOI | MR | Zbl

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

[9] S. Konstein, I. Tyutin, Cohomologies of the Poisson superalgebra on $(2,n)$-superdimensional spaces, E-print hep-th/0411235 | MR

[10] S. Konstein, I. Tyutin, Deformation of the central extension of the Poisson superalgebra, E-print hep-th/0501027 | MR

[11] M. Scheunert, R. B. Zhang, J. Math. Phys., 39 (1998), 5024 ; E-print q-alg/9701037 | DOI | MR | Zbl

[12] S. Konstein, A. Smirnov, I. Tyutin, General form of deformation of Poisson superbracket, E-print hep-th/0401023

[13] S. Konstein, A. Smirnov, I. Tyutin, Cohomologies of the Poisson superalgebra, E-print hep-th/0312109

[14] L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. I, Mir, M., 1986 | MR