Abstract
Let be the twisted Heisenberg–Virasoro algebra. In this paper, we first present a method to produce a class of tensor product -modules, by which we can obtain the known weight -modules and non-weight -modules . Then we study a class of linear tensor product non-weight modules over . The necessary and sufficient conditions for to be irreducible are obtained. We also determine the necessary and sufficient conditions for two such irreducible -modules to be isomorphic.
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