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

Author： Fraj N.  

Publisher： Springer Publishing Company

ISSN： 0040-5779

Source： Theoretical and Mathematical Physics, Vol.163, Iss.2, 2010-05, pp. : 618-633

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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 SΨD(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 SΨD(S 1|2 ).

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