Simple Weight Modules Over The Twisted Heisenberg-virasoro Algebra

Let(?)be the the twisted Heisenberg-Virasoro algebra.In this paper,we first constructed and classified the simple weight modules over the 7-dimensional solvable Lie algebra b1 related to(?).Then we determined the simplicity of a class of(?)modules with l0/z2-1?Z+ and determined their simple quotient when they were not simple.We also constructed some explicit examples of such kind of modules by using the simple weight module over b1.