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Non-weight modules over the super Schrödinger algebra
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 647-664
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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.
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.
DOI : 10.21136/CMJ.2024.0030-23
Classification : 17B10, 17B20, 17B35, 17B66
Keywords: super Schrödinger algebra; simple module; U($\mathfrak {h}$)-free module, non-weight module 
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     title = {Non-weight modules over the super {Schr\"odinger} algebra},
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     year = {2024},
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Wang, Xinyue; Chen, Liangyun; Ma, Yao. Non-weight modules over the super Schrödinger algebra. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 647-664. doi: 10.21136/CMJ.2024.0030-23

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