Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal algebra relative to the locality $N=2$. In order to obtain this result we adjust the algebraic discrete Morse theory to the case of differential algebras.