Graded Identities for the Adjoont Representation of $sl_2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913570275459072 |
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| author | Sampaio, Cássia F. Koshlukov, Plamen E. |
| author_facet | Sampaio, Cássia F. Koshlukov, Plamen E. |
| contents | Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of $\mathfrak{sl}_2 (K)$, or equivalently, the $\mathbb{Z}_2$-graded identities for the pair $(M_3(K), \mathfrak{sl}_2 (K))$. We work with the canonical grading on $\mathfrak{sl}_2 (K)$ and the only nontrivial $\mathbb{Z}_2$-grading of the associative algebra $M_3(K)$ induced by that on $\mathfrak{sl}_2(K)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_00811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded Identities for the Adjoont Representation of $sl_2$ Sampaio, Cássia F. Koshlukov, Plamen E. Rings and Algebras Representation Theory 17B01, 17B70, 16R10, 16R50 Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of $\mathfrak{sl}_2 (K)$, or equivalently, the $\mathbb{Z}_2$-graded identities for the pair $(M_3(K), \mathfrak{sl}_2 (K))$. We work with the canonical grading on $\mathfrak{sl}_2 (K)$ and the only nontrivial $\mathbb{Z}_2$-grading of the associative algebra $M_3(K)$ induced by that on $\mathfrak{sl}_2(K)$. |
| title | Graded Identities for the Adjoont Representation of $sl_2$ |
| topic | Rings and Algebras Representation Theory 17B01, 17B70, 16R10, 16R50 |
| url | https://arxiv.org/abs/2411.00811 |