Abstract
We use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules over the Heisenberg-Virasoro algebra L. These modules contain the highest weight modules and Whittaker modules. Then we precisely characterize the simple restricted modules over L under certain conditions. We know that simple modules over the two dimensional non-abelian Lie algebra are classified by R. Block in [10]. We also give a complete classification of simple modules for a three dimensional solvable Lie algebra.
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