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Two classes of non-weight modules over the twisted Heisenberg–Virasoro algebra

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Abstract

We study two classes of non-weight modules \(\Omega (\lambda ,\alpha ,\beta )\otimes \mathrm {Ind}(M)\) and \({\mathcal {M}}\big (V,\Omega (\lambda ,\alpha ,\beta )\big )\) over the twisted Heisenberg–Virasoro algebra in this paper. We present conditions under which these modules are irreducible, the necessary and sufficient conditions under which modules in each class are isomorphic, and also show that the irreducible modules in these two classes are new. Finally, we construct non-weight modules \(\mathrm {Ind}_{{\underline{y}},\lambda }({\mathbb {C}}_{RS})\) and \(\mathrm {Ind}_{{\underline{z}},\lambda }({\mathbb {C}}_{PQ})\) over the twisted Heisenberg–Virasoro algebra and then apply the established results to give irreducible conditions for these modules.

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Acknowledgements

The authors would like to thank the referee very much for valuable suggestions and comments to put this paper in better shape. Jianzhi Han was partially supported by the NSFC (11501417, 11671247). Yucai Su and Xiaoqing Yue were partially supported by the NSFC (11431010).

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Authors and Affiliations

  1. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China

    Haibo Chen

  2. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Jianzhi Han, Yucai Su & Xiaoqing Yue

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  1. Haibo Chen
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  2. Jianzhi Han
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  3. Yucai Su
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  4. Xiaoqing Yue
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Correspondence to Jianzhi Han.

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Chen, H., Han, J., Su, Y. et al. Two classes of non-weight modules over the twisted Heisenberg–Virasoro algebra. manuscripta math. 160, 265–284 (2019). https://doi.org/10.1007/s00229-018-1059-3

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