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arXiv · 2411.00811

Graded Identities for the Adjoont Representation of $sl_2$

Cássia F. Sampaio·Plamen E. Koshlukov
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Abstract

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 $\mathfrak{sl}_2(K)$.

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Cássia F. Sampaio, Plamen E. Koshlukov. 2024-10-24. Graded Identities for the Adjoont Representation of $sl_2$. https://arxiv.org/abs/2411.00811

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