Two classes of non-weight modules over the twisted Heisenberg–Virasoro algebra.

We study two classes of non-weight modules Ω (λ , α , β) ⊗ Ind (M) and M (V , Ω (λ , α , β)) over the twisted Heisenberg–Virasoro algebra in this paper. We present conditions under which these modules are irreducible, the necessary and sufficient conditions under which modules in each class are isomorphic, and also show that the irreducible modules in these two classes are new. Finally, we construct non-weight modules Ind y ̲ , λ (C RS) and Ind z ̲ , λ (C PQ) over the twisted Heisenberg–Virasoro algebra and then apply the established results to give irreducible conditions for these modules. [ABSTRACT FROM AUTHOR]