Cohomology of finite Lie conformal algebras

By using the energy operator introduced by Bakalov, De Sole, and Kac, we propose an algorithm for computing the cohomology of finitely generated free Lie conformal algebras with a Virasoro element. This computational method enables us to compute cohomologies with coefficients in their conformal modules, especially in adjoint modules. As concrete applications, we compute by Mathematica both basic and reduced cohomologies for the W(b), Schrödinger–Virasoro and extended Schrödinger–Virasoro Lie conformal algebras.