Representations for the Nongraded Virasoro-Like Algebra

Abstract

It is proved in this article that an irreducible module over the nongraded Virasoro-like algebra ℒ, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, we give the complete classification of indecomposable ℒ-modules which satisfy L _{r, s} v _{m, n}  ⊆ ℂv _{r+m, s+n+1} + ℂv _{r+m, s+n} .

Key Words:

• GHW module
• Module of intermediate series
• Nongraded Virasoro-like algebra
• Uniformly bounded module

2000 Mathematics Subject Classification:

• Primary 17B67
• Secondary 17B68

ACKNOWLEDGMENTS

Project is supported in part by China NSF grants 10931006, 10871125 and a grant of Science and Technology Commission of Shanghai Municipality (No. 09XD1402500).