Geodesic
Deforming the~Lie superalgebra of contact vector fields on $S^{1|2}$ inside the~Lie superalgebra of pseudodifferential operators on $S^{1|2}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 258-276

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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. 
@article{TMF_2010_163_2_a2,
     author = {N. Ben Fraj and S. Omri},
     title = {Deforming {the~Lie} superalgebra of contact vector fields on $S^{1|2}$ inside {the~Lie} superalgebra of pseudodifferential operators on $S^{1|2}$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {258--276},
     publisher = {mathdoc},
     volume = {163},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a2/}
}
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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 $S^{1|2}$. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 258-276. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a2/