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Czechoslovak Mathematical Journal, Vol. 74, No. 3, pp. 647-664, 2024

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma

Received January 19, 2023.   Published online August 28, 2024.
Abstract:  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.
Keywords:  super Schrödinger algebra; simple module; U($\mathfrak{h}$)-free module, non-weight module
Classification MSC:  17B10, 17B20, 17B35, 17B66
DOI:  10.21136/CMJ.2024.0030-23
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Affiliations:   Xinyue Wang, Liangyun Chen, Yao Ma (corresponding author), School of Mathematics and Statistics, Northeast Normal University, No. 5268, Renmin Street, Changchun 130024, Jilin, P. R. China, e-mail: wangxy741@nenu.edu.cn, chenly640@nenu.edu.cn, may703@nenu.edu.cn
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