S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “Cohomologies of the Poisson superalgebra”, TMF, 143:2 (2005), 163–194; Theoret. and Math. Phys., 143:2 (2005), 625

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 143, Number 2, Pages 163–194
DOI: https://doi.org/10.4213/tmf1809 (Mi tmf1809)

This article is cited in 12 scientific papers (total in 12 papers)

Cohomologies of the Poisson superalgebra

S. E. Konstein, A. G. Smirnov, I. V. Tyutin

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Full-text PDF (387 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf1809

Abstract: 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, Poisson superalgebra, cohomologies, deformation,

$*$ -commutator, quantization.

Received: 13.10.2004

English version:
Theoretical and Mathematical Physics, 2005, Volume 143, Issue 2, Pages 625–650
DOI: https://doi.org/10.1007/s11232-005-0095-9

Bibliographic databases:

Language: Russian

Citation: S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “Cohomologies of the Poisson superalgebra”, TMF, 143:2 (2005), 163–194; Theoret. and Math. Phys., 143:2 (2005), 625–650

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1809

https://doi.org/10.4213/tmf1809

https://www.mathnet.ru/eng/tmf/v143/i2/p163

This publication is cited in the following 12 articles:

Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites, “Deformations of Symmetric Simple Modular Lie (Super)Algebras”, SIGMA, 19 (2023), 031, 66 pp.
S. E. Konstein, I. V. Tyutin, “Deformations of the antibracket with Grassmann-valued deformation parameters”, Theoret. and Math. Phys., 183:1 (2015), 501–515
V. V. Zharinov, “Cohomologies of spaces of Schwartz test functions”, Theoret. and Math. Phys., 170:3 (2012), 263–273
S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “Hochschild cohomologies and deformations of the pointwise superproduct”, Theoret. and Math. Phys., 158:3 (2009), 271–292
S. E. Konstein, I. V. Tyutin, “Deformations of the nondegenerate constant Poisson bracket and antibracket on superspaces of an arbitrary superdimension”, Theoret. and Math. Phys., 155:1 (2008), 598–605
S. E. Konstein, I. V. Tyutin, “General form of the deformation of the Poisson superbracket on a $(2,n)$-dimensional superspace”, Theoret. and Math. Phys., 155:2 (2008), 734–753
S. E. Konstein, I. V. Tyutin, “Deformations of the central extension of the Poisson superalgebra”, Theoret. and Math. Phys., 156:2 (2008), 1180–1198
Konstein, SE, “Deformations and central extensions of the antibracket superalgebra”, Journal of Mathematical Physics, 49:7 (2008), 072103
S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “General form of the deformation of the Poisson superbracket”, Theoret. and Math. Phys., 148:2 (2006), 1011–1024
S. E. Konstein, I. V. Tyutin, “Cohomology of the Poisson Superalgebra on Spaces of Superdimension $(2,n_-)$”, Theoret. and Math. Phys., 145:3 (2005), 1619–1645
Konstein, SE, “Cohomologies of the Poisson superalgebra (vol 143, pg 628, 2005)”, Theoretical and Mathematical Physics, 144:3 (2005), 1372
S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “Cohomologies of the Poisson superalgebra”, Theoret. and Math. Phys., 143:2 (2005), 625–650

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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