V. V. Zharinov, “Cohomology of a Poisson Algebra”, TMF, 136:2 (2003), 179–196; Theoret. and Math. Phys., 136:2 (2003), 1049

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 136, Number 2, Pages 179–196
DOI: https://doi.org/10.4213/tmf228 (Mi tmf228)

This article is cited in 8 scientific papers (total in 8 papers)

Cohomology of a Poisson Algebra

V. V. Zharinov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (317 kB) Citations (8)

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DOI: https://doi.org/10.4213/tmf228

Abstract: We propose a technique for calculating the cohomology of a Poisson algebra using the Laplace transformation of distributions with compact support. We find the lowest-order cohomologies of this algebra with coefficients in two natural representations: the trivial and the adjoint representations.

Keywords: Lie algebras, Poisson algebras, cohomology.

Received: 15.12.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 136, Issue 2, Pages 1049–1065
DOI: https://doi.org/10.1023/A:1025024803020

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Zharinov, “Cohomology of a Poisson Algebra”, TMF, 136:2 (2003), 179–196; Theoret. and Math. Phys., 136:2 (2003), 1049–1065

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf228

https://doi.org/10.4213/tmf228

https://www.mathnet.ru/eng/tmf/v136/i2/p179

This publication is cited in the following 8 articles:

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
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, “Cohomologies of the Poisson superalgebra”, Theoret. and Math. Phys., 143:2 (2005), 625–650
V. V. Zharinov, “Hochschild Cohomology of the Algebra of Smooth Functions on the Torus”, Theoret. and Math. Phys., 144:3 (2005), 1247–1263
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
V. V. Zharinov, “Hochschild Cohomology of the Algebra of Smooth Functions on the Torus”, Theor Math Phys, 144:3 (2005), 1247
V. V. Zharinov, “Hochschild Cohomologies of the Algebra of Smooth Functions”, Theoret. and Math. Phys., 140:3 (2004), 1195–1204

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

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