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TMF, 2006, Volume 148, Number 2, Pages 163–178 (Mi tmf2078)  

This article is cited in 4 scientific papers (total in 4 papers)

General form of the deformation of the Poisson superbracket

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

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

Abstract: All continuous formal deformations of the Poisson algebra realized on Grassmann-valued compactly supported smooth functions on $\mathbb R^{2n}$ with $2n\ge4$ are found up to an equivalence transformation. We show that in the algebras considered, there exist additional deformations that differ from the Moyal bracket.

Keywords: Grassmann algebra, Poisson superalgebra, central extension, cohomologies, $*$-commutator, deformation, quantization

DOI: https://doi.org/10.4213/tmf2078

Full text: PDF file (493 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 148:2, 1011–1024

Bibliographic databases:

Received: 12.12.2005

Citation: S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “General form of the deformation of the Poisson superbracket”, TMF, 148:2 (2006), 163–178; Theoret. and Math. Phys., 148:2 (2006), 1011–1024

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. S. E. Konstein, I. V. Tyutin, “Deformations of the central extension of the Poisson superalgebra”, Theoret. and Math. Phys., 156:2 (2008), 1180–1198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. V. Zharinov, “Cohomologies of spaces of Schwartz test functions”, Theoret. and Math. Phys., 170:3 (2012), 263–273  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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