Centers of Universal Enveloping Algebras
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916245598633984 |
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| author | Yang, Yaping Zeng, Daihao |
| author_facet | Yang, Yaping Zeng, Daihao |
| contents | The universal enveloping algebra $U(\mathfrak{g} )$ of a current (super)algebra or loop (super)algebra $\mathfrak{g} $ is considered over an algebraically closed field $\mathbb{K} $ with characteristic $p\ge 0$. This paper focuses on the structure of the center $Z(\mathfrak{g} )$ of $U(\mathfrak{g} )$. In the case of zero characteristic, $Z(\mathfrak{g} )$ is generated by the centers of $\mathfrak{g} $. In the case of prime characteristic, $Z(\mathfrak{g} )$ is generated by the centers of $\mathfrak{g} $ and the $p$-centers of $U(\mathfrak{g} )$. We also study the structure of $Z(\mathfrak{g} )$ in the semisimple Lie (super)algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Centers of Universal Enveloping Algebras Yang, Yaping Zeng, Daihao Representation Theory Rings and Algebras The universal enveloping algebra $U(\mathfrak{g} )$ of a current (super)algebra or loop (super)algebra $\mathfrak{g} $ is considered over an algebraically closed field $\mathbb{K} $ with characteristic $p\ge 0$. This paper focuses on the structure of the center $Z(\mathfrak{g} )$ of $U(\mathfrak{g} )$. In the case of zero characteristic, $Z(\mathfrak{g} )$ is generated by the centers of $\mathfrak{g} $. In the case of prime characteristic, $Z(\mathfrak{g} )$ is generated by the centers of $\mathfrak{g} $ and the $p$-centers of $U(\mathfrak{g} )$. We also study the structure of $Z(\mathfrak{g} )$ in the semisimple Lie (super)algebra. |
| title | Centers of Universal Enveloping Algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2405.08325 |