Representations of non-finitely graded Lie algebras related to Virasoro algebra
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916270486585344 |
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| author | Xia, Chunguang Ma, Tianyu Dong, Xiao Zhang, Mingjing |
| author_facet | Xia, Chunguang Ma, Tianyu Dong, Xiao Zhang, Mingjing |
| contents | In this paper, we study representations of non-finitely graded Lie algebras $\mathcal{W}(ε)$ related to Virasoro algebra, where $ε= \pm 1$. Precisely speaking, we completely classify the free $\mathcal{U}(\mathfrak h)$-modules of rank one over $\mathcal{W}(ε)$,and find that these module structures are rather different from those of other graded Lie algebras. We also determine the simplicity and isomorphism classes of these modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of non-finitely graded Lie algebras related to Virasoro algebra Xia, Chunguang Ma, Tianyu Dong, Xiao Zhang, Mingjing Representation Theory In this paper, we study representations of non-finitely graded Lie algebras $\mathcal{W}(ε)$ related to Virasoro algebra, where $ε= \pm 1$. Precisely speaking, we completely classify the free $\mathcal{U}(\mathfrak h)$-modules of rank one over $\mathcal{W}(ε)$,and find that these module structures are rather different from those of other graded Lie algebras. We also determine the simplicity and isomorphism classes of these modules. |
| title | Representations of non-finitely graded Lie algebras related to Virasoro algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2403.04213 |