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

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , 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 ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles of the group...

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