Induced modules and central character quotients for Takiff $\mathfrak{sl}_{2}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917579353751552 |
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| author | Zhu, Xiaoyu |
| author_facet | Zhu, Xiaoyu |
| contents | We construct a large new family of simple modules over Takiff $\mathfrak{sl}_{2}$. We prove that the quotient of the universal enveloping algebra of the Takiff Lie algebra for $\mathfrak{sl}_{2}$ by the ideal generated by a non-trivial central character is a simple algebra. In the case of the trivial central character, we show that the corresponding ideal is primitive by explicitly constructing a simple module whose annihilator coincides with that ideal. Together with the annihilators of simple $\mathfrak{sl}_{2}$-modules, we expect that the above ideals exhaust all primitive ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Induced modules and central character quotients for Takiff $\mathfrak{sl}_{2}$ Zhu, Xiaoyu Representation Theory We construct a large new family of simple modules over Takiff $\mathfrak{sl}_{2}$. We prove that the quotient of the universal enveloping algebra of the Takiff Lie algebra for $\mathfrak{sl}_{2}$ by the ideal generated by a non-trivial central character is a simple algebra. In the case of the trivial central character, we show that the corresponding ideal is primitive by explicitly constructing a simple module whose annihilator coincides with that ideal. Together with the annihilators of simple $\mathfrak{sl}_{2}$-modules, we expect that the above ideals exhaust all primitive ideal. |
| title | Induced modules and central character quotients for Takiff $\mathfrak{sl}_{2}$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2401.17627 |