Simple restricted modules for the Heisenberg-Virasoro algebra

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 Lunder 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. (C) 2021 Elsevier Inc. All rights reserved.