Tensor product modules over the planar Galilean conformal algebra from free modules of rank one
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| Format: | Preprint |
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2025
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| _version_ | 1866909651843416064 |
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| author | Cheng, Jin Gao, Dongfang Zeng, Ziting |
| author_facet | Cheng, Jin Gao, Dongfang Zeng, Ziting |
| contents | In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra $\mathcal{G}$ named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in $(2+1)$ dimensional space-time. We give the necessary and sufficient conditions for the tensor product modules of any two of $\mathcal{U}(\mathfrak{h})$-free modules of rank one over $\mathcal{G}$ to be irreducible, where $\mathfrak{h}$ is the Cartan subalgebra of $\mathcal{G}$.Furthermore, the isomorphism classes of these irreducible tensor product modules are determined. As an application, we obtain the necessary conditions for the tensor product modules of any two of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank one over Witt algebra and Heisenberg-Virasoro algebra to be irreducible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor product modules over the planar Galilean conformal algebra from free modules of rank one Cheng, Jin Gao, Dongfang Zeng, Ziting Representation Theory 17B10, 17B65, 17B66, 17B68 In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra $\mathcal{G}$ named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in $(2+1)$ dimensional space-time. We give the necessary and sufficient conditions for the tensor product modules of any two of $\mathcal{U}(\mathfrak{h})$-free modules of rank one over $\mathcal{G}$ to be irreducible, where $\mathfrak{h}$ is the Cartan subalgebra of $\mathcal{G}$.Furthermore, the isomorphism classes of these irreducible tensor product modules are determined. As an application, we obtain the necessary conditions for the tensor product modules of any two of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank one over Witt algebra and Heisenberg-Virasoro algebra to be irreducible. |
| title | Tensor product modules over the planar Galilean conformal algebra from free modules of rank one |
| topic | Representation Theory 17B10, 17B65, 17B66, 17B68 |
| url | https://arxiv.org/abs/2506.14893 |