A family of simple weight modules over the Virasoro algebra

Using simple modules over the derivation Lie algebra C[t]ddt for the polynomial algebra C[t], we construct new weight modules over the Witt algebra where all the weight spaces are infinite dimensional. We determine the necessary and sufficient conditions for these new modules being simple, as well as determining the necessary and sufficient conditions for two Witt modules being isomorphic. If a module is not simple, we obtain all its submodules. As a consequence, we fully determine the simplicity and isomorphism classes for the Witt modules defined by [3], which are a small proportion of the modules constructed in this study.