超薛定谔代数上的非重模块

Pub Date : 2024-08-28 DOI:10.21136/cmj.2024.0030-23

Xinyue Wang, Liangyun Chen, Yao Ma

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引用次数: 0

摘要

我们构建了一个非重模块族，它们是(1+1)维时空中N = 1超薛定谔代数上秩为2的自由（U(\frak{h})\）模块。我们确定了这些模块的同构类。特别是，我们还构造并分类了在（1+1维时空）的N = 1超薛定谔代数上的秩为2的自由（U(\frak{h})\）模块。此外，我们还得到了这些模块是简单模块的充分必要条件。

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Non-weight modules over the super Schrödinger algebra

We construct a family of non-weight modules which are free \(U(\frak{h})\)-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 \(U(\frak{h})\)-modules of rank 2 over \(\frak{osp}(1\mid 2)\) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

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