Graded modules for Virasoro-like algebra

Abstract

In this paper, we consider the classification of irreducible $\mathbf{Z}$- and ${\mathbf{Z}}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight irreducible modules. As a consequence, we also determine all the modules with nonzero center. Finally, we prove that there does not exist any nontrivial $\mathbf{Z}$-graded modules of intermediate series.

17pages, 0 figures