Partial classification of cuspidal simple modules for Virasoro-like algebra

Let PP be the Lie algebra of Hamiltonian vector fields on the torus, which is also known as the Virasoro-like algebra, a special kind of the so-called Block type Lie algebra. And let AA be the Laurent polynomial algebra in two variables. In this paper, by following S.E. Rao's strategy of “backward induction”, we prove that any quasi-finite simple (A,P)(A,P)-module has to come from Larsson–Shen's construction.