Abstract
In this paper, we denote the semi-direct product of the Witt algebra and the loop Schrödinger algebra by \(\cal{SW}(b)\), where b belongs to ℂ. Our primary focus is on classifying U(ℂd0 ⊕ ℂh0)-free modules of rank 1 over \(\cal{SW}(b)\). We characterize both the irreducibility and isomorphism classes of these modules. Furthermore, we construct new non-weight modules over \(\cal{SW}(0)\) by taking the tensor product of U(ℂd0 ⊕ ℂh0)-free modules with irreducible highest weight modules. We also consider the irreducibility and isomorphism classes for the tensor product modules. Finally, we reformulate some tensor product modules over \(\cal{SW}(0)\) as induced modules derived from modules over certain subalgebras.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 12271085 and 12071405), National Science Foundation of Jilin Province (Grant No. YDZJ202201ZYTS589), and the Fundamental Research Funds for the Central Universities. The authors wish to express their appreciation to the referees for their helpful suggestions, which have markedly improved this paper.
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Liu, Y., Wang, X., Ma, Y. et al. Non-weight modules over the algebra \(\cal{SW}(b)\). Sci. China Math. (2024). https://doi.org/10.1007/s11425-023-2317-0
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DOI: https://doi.org/10.1007/s11425-023-2317-0