Graded modules for Virasoro-like algebra

Details Graded modules for Virasoro-like algebra Graded modules for Virasoro-like algebra

2007-12-02

arxiv.org/abs/0712.0144v1

Mathematics

Representation Theory

17pages, 0 figures

Scientific paper

In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-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 ${\bf Z}$-graded modules of intermediate series.

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