Wajd Afsi

On the third cohomology of the Lie algebra of vector fields on weighted densities on R

Let Vect($\mathbb{R}$) be the Lie algebra of smooth vector fields on $\mathbb{R}$ and $\mathbb{F}_λ$ be the space of $λ$-densities on $\mathbb{R}$. Vect($\mathbb{R}$) acts on $\mathbb{F}_λ$ by Lie derivative. In this paper, we compute the third differential cohomology of the Lie algebra Vect($\mathbb{R}$) with coeffcients in the space $\mathbb{F}_λ.$ Explicit cocycles spanning these cohomology spaces are given.