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

Abstract

The relative cohomology Hdiff1(K(1|3), osp(2, 3);Dγ,µ(S1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators Dγ,µ(S1|3) acting on tensor densities on S1|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(Xf) = D1D2D3(f)α31/2, Xf ∈ K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3).