Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra

Abstract

In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.