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Keywords:
super Schrödinger algebra; simple module; U($\mathfrak {h}$)-free module, non-weight module
super Schrödinger algebra; simple module; U($\mathfrak {h}$)-free module, non-weight module
Summary:
We construct a family of non-weight modules which are free $U(\mathfrak {h})$-modules of rank 2 over the $N=1$ super Schrödinger algebra in $(1+1)$-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free $U(\mathfrak {h})$-modules of rank 2 over $\mathfrak {osp}(1|2)$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
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