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TMF, 2010, Volume 163, Number 2, Pages 258–276 (Mi tmf6498)  

This article is cited in 6 scientific papers (total in 6 papers)

Deforming the Lie superalgebra of contact vector fields on $S^{1|2}$ inside the Lie superalgebra of pseudodifferential operators on $S^{1|2}$

N. Ben Fraja, S. Omriba

a Institut Supérieur des Sciences Appliquées et Technologie, Sousse, Tunisie
b Département de Mathématiques, Faculté des Sciences de Gafsa, Gafsa, Tunisie

Abstract: We classify deformations of the standard embedding of the Lie superalgebra $\mathcal K(2)$ of contact vector fields on the $(1,2)$-dimensional supercircle into the Lie superalgebra $S\Psi D(S^{1|2})$ of pseudodifferential operators on the supercircle $S^{1|2}$. The proposed approach leads to the deformations of the central charge induced on $\mathcal K(2)$ by the canonical central extension of $S\Psi D(S^{1|2})$.

Keywords: cohomology, Lie superalgebra, Lie superalgebra deformation

DOI: https://doi.org/10.4213/tmf6498

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English version:
Theoretical and Mathematical Physics, 2010, 163:2, 618–633

Bibliographic databases:

Received: 07.10.2009
Revised: 05.11.2009

Citation: N. Ben Fraj, S. Omri, “Deforming the Lie superalgebra of contact vector fields on $S^{1|2}$ inside the Lie superalgebra of pseudodifferential operators on $S^{1|2}$”, TMF, 163:2 (2010), 258–276; Theoret. and Math. Phys., 163:2 (2010), 618–633

Citation in format AMSBIB
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\by N.~Ben Fraj, S.~Omri
\paper Deforming the~Lie superalgebra of contact vector fields on $S^{1|2}$ inside the~Lie superalgebra of pseudodifferential operators on $S^{1|2}$
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\yr 2010
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\pages 258--276
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  • https://doi.org/10.4213/tmf6498
  • http://mi.mathnet.ru/eng/tmf/v163/i2/p258

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

    This publication is cited in the following articles:
    1. Basdouri I., “First Space Cohomology of the Orthosymplectic Lie Superalgebra in the Lie Superalgebra of Superpseudodifferential Operators”, Algebr. Represent. Theory, 16:1 (2013), 35–50  crossref  mathscinet  zmath  isi  scopus
    2. Ncib O., Omri S., “Deforming the Orthosymplectic Lie Superalgebra Inside the Lie Superalgebra of Superpseudodifferential Operators”, J. Geom. Phys., 86 (2014), 211–221  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Belghith N., Ben Ammar M., Ben Fraj N., “Differential Operators on the Weighted Densities on the Supercircle S-1 Vertical Bar 1”, Stud. Sci. Math. Hung., 52:4 (2015), 477–503  crossref  mathscinet  zmath  isi  scopus
    4. Ncib O., Omri S., “Second cohomology space of the orthosymplectic Lie superalgebra with coefficients in the Lie superalgebra of superpseudodifferential operators”, J. Geom. Phys., 107 (2016), 99–113  crossref  mathscinet  zmath  isi  scopus
    5. Basdouri O., “Deformation of
      $$\mathfrak {aff}(1)$$
      aff ( 1 ) -modules of pseudo-differential operators and symbols”, J. Pseudo-Differ. Oper. Appl., 7:2 (2016), 157–179  crossref  mathscinet  zmath  isi  scopus
    6. Hamza R., Selmi Z., Boujelben J., “Differential operators on the supercircle S1|2 and symbol map”, Int. J. Geom. Methods Mod. Phys., 14:1 (2017), 1750002  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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