A class of simple weight Virasoro modules

作者：Liu, Genqiang; Lu, Rencai^*; Zhao, Kaiming

来源：Journal of Algebra, 2015, 424: 506-521.

DOI：10.1016/j.jalgebra.2014.08.054

• Virasoro algebra
• Weight module
• Simple module

For a simple module M over the positive part of the Virasoro algebra (actually for any simple module over some finite dimensional solvable Lie algebras a(r)) and any alpha is an element of C, a class of weight modules N(M, alpha) over the Virasoro algebra is constructed. These weight modules have infinite dimensional weight spaces if dim M > 1. The necessary and sufficient conditions for N(M, alpha) to be simple are obtained. We also determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. Many examples for such irreducible Virasoro modules with different features are provided. In particular the irreducible weight Virasoro modules Gamma(alpha(1), alpha(2), lambda(1), lambda(2)) are defined on the polynomial algebra C[x]circle times C[t, t(-1)] for any alpha(1), alpha(2), lambda(1), lambda(2) is an element of C with lambda(1) or lambda(2) nonzero. By twisting the weight modules N(M, alpha) we also obtain nonweight simple Virasoro modules N(M, beta) for any nonconstant beta is an element of C[t, t(-1)].

• 单位
  苏州大学; 河南大学