1-Cocycles on the group of contactomorphisms on the supercircle S1|3 generalizing the Schwarzian derivative

The relative cohomology H_diff¹(K(1|3), osp(2, 3);D_γ,µ(S^1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators D_γ,µ(S^1|3) acting on tensor densities on S^1|3, is calculated in N.Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1-cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1-cocycle s(X_f) = D₁D₂D₃(_f)α₃^1/2, X^f ∈ K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3).