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Let Vect (R) be the Lie algebra of smooth vector fields on R and F_ be the space of -densities on R. Vect (R) acts on F_ by Lie derivative. In this paper, we compute the third differential cohomology of the Lie algebra Vect (R) with coeffcients in the space F_. Explicit cocycles spanning these cohomology spaces are given.
Afsi et al. (Sun,) studied this question.