Deformations of the central extension of the Poisson superalgebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 250-269
Cet article a éte moissonné depuis la source Math-Net.Ru
The Poisson superalgebra realized on smooth Grassmann-valued functions with compact support has a central extension at some values of the superdimension. We find formal deformations of these central extensions.
Keywords:
Grassmann algebra, central extension, cohomology, deformation, $*$-commutator.
Mots-clés : Poisson superalgebra, quantization
Mots-clés : Poisson superalgebra, quantization
@article{TMF_2008_156_2_a7,
author = {S. E. Konstein and I. V. Tyutin},
title = {Deformations of the~central extension of {the~Poisson} superalgebra},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {250--269},
year = {2008},
volume = {156},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a7/}
}
S. E. Konstein; I. V. Tyutin. Deformations of the central extension of the Poisson superalgebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 250-269. http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a7/
[1] S. E. Konshtein, A. G. Smirnov, I. V. Tyutin, TMF, 143:2 (2005), 163–194 | DOI | MR
[2] S. E. Konshtein, A. G. Smirnov, I. V. Tyutin, TMF, 148:2 (2006), 163–178 | DOI | MR
[3] S. E. Konshtein, I. V. Tyutin, TMF, 145:3 (2005), 291–320 | DOI | MR
[4] S. E. Konshtein, I. V. Tyutin, TMF, 155:2 (2008), 265–286 ; General form of the deformation of the Poisson superbracket on $(2,n)$-dimensional superspace, arXiv: hep-th/0610308 | DOI | MR
[5] M. Scheunert, R. B. Zhang, J. Math. Phys., 39:9 (1998), 5024–5061 ; arXiv:q-alg/9701037 | DOI | MR | Zbl
[6] M. Gerstenhaber, Ann. of Math. (2), 79:1 (1964), 59–103 ; 99:2 (1974), 257–276 | DOI | MR | Zbl | DOI | MR | Zbl