In this paper, we mainly study free U(h)-modules over the N=1 Heisenberg–Virasoro superalgebra. We construct a family of non-weight modules that are free of rank 2 when regarded as modules over the Cartan subalgebra. Moreover, we classify the free U(h)-modules of rank 2 over the N = 1 Heisenberg–Virasoro superalgebra and provide the necessary and sufficient conditions for such g-modules to be isomorphic.
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Dilxat et al. (2024) studied this question.
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