Deforming the Lie Superalgebra of Contact Vector Fields on $S^{1|1}$

Boujemaa Agrebaoui (1) , Nizar Ben Fraj (1) , Salem Omri (1)

1 Laboratoire d'Analyse Harmonique de Sfax

We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie superalgebra of superpseudodifferential operators on the supercircle. This approach leads to the deformations of the central charge induced on K(1) by the canonical central extension of $S\Psi DO$.

Domaines: Physique mathématique [math-ph]

Boujemaa Agrebaoui, Nizar Ben Fraj, Salem Omri. Deforming the Lie Superalgebra of Contact Vector Fields on $S^{1|1}$. Journal of Nonlinear Mathematical Physics, 2006, 13, pp.no. 1, 19--33. ⟨hal-00021589⟩