Representations of non-finitely graded Heisenberg-Virasoro type Lie algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913539225026560 |
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| author | Xia, Chunguang Ma, Tianyu Wang, Wei Zhang, Mingjing |
| author_facet | Xia, Chunguang Ma, Tianyu Wang, Wei Zhang, Mingjing |
| contents | We construct and study non-finitely graded Lie algebras $\mathcal{HV}(a,b;ε)$ related to Heisenberg-Virasoro type Lie algebras, where $a,b$ are complex numbers, and $ε= \pm 1$. Using combinatorial techniques, we completely classify the free $\mathcal{U}(\mathfrak h)$-modules of rank one over $\mathcal{HV}(a,b;ε)$. It turns out that these modules are more varied and complex than those over non-finitely graded Virasoro algebras, and in particular admit infinitely many free parameters if $b=1$ and $ε=-1$. Meanwhile, we also determine the simplicity and isomorphism classes of these modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06862 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of non-finitely graded Heisenberg-Virasoro type Lie algebras Xia, Chunguang Ma, Tianyu Wang, Wei Zhang, Mingjing Representation Theory We construct and study non-finitely graded Lie algebras $\mathcal{HV}(a,b;ε)$ related to Heisenberg-Virasoro type Lie algebras, where $a,b$ are complex numbers, and $ε= \pm 1$. Using combinatorial techniques, we completely classify the free $\mathcal{U}(\mathfrak h)$-modules of rank one over $\mathcal{HV}(a,b;ε)$. It turns out that these modules are more varied and complex than those over non-finitely graded Virasoro algebras, and in particular admit infinitely many free parameters if $b=1$ and $ε=-1$. Meanwhile, we also determine the simplicity and isomorphism classes of these modules. |
| title | Representations of non-finitely graded Heisenberg-Virasoro type Lie algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.06862 |