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arXiv · 2008.03860

$\mathbb{Z}_3$-graded identities of the pair $(M_3(K),gl_3(K))$

Luís Felipe Gonçalves Fonseca
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Abstract

Let $M_n(K)$ be the algebra of $n \times n$ matrix over an infinite integral domain $K$. Let $gl_n(K)$ be the Lie algebra of $n \times n$ matrix with the usual Lie product over $K$. Let $G = \{g_1,\ldots,g_n\}$ be a group of order $n$. We describe the polynomials that form a basis for the $G$-graded identities of the pair $(M_n(K),gl_n(K))$ with an elementary $G$-grading induced by the $n$-tuple $(g_1,\ldots,g_n)$. In the end, we describe an explicit basis for the $\mathbb{Z}_3$-graded identities of the pair $(M_3(K),gl_3(K))$.

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BibTeXRIS

Luís Felipe Gonçalves Fonseca. 2020-08-10. $\mathbb{Z}_3$-graded identities of the pair $(M_3(K),gl_3(K))$. https://arxiv.org/abs/2008.03860

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