Abstract
Super W -algebra SW ( 3 2 , 3 2 ) is the supersymmetric extension of Galilean conformal algebra in 2d. In this paper, we obtain that super W -algebra SW ( 3 2 , 3 2 ) admits only triangular coboundary Lie super-bialgebra structures and the proof is mainly based on the computation of the first cohomology group of SW ( 3 2 , 3 2 ) with coefficients in the tensor product of its adjoint module.
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