Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra W(ϱ)[s]W(ϱ)[s] for s=0,12. With this result and method, we can also do such works for some Lie algebras related to the Virasoro algebra, including the several kinds of Schrödinger–Virasoro Lie algebras, which are open up to now.