论文标题
$ \ mathbb {z} _3 $ - $（m_3（k），gl_3（k））$的划分身份
$\mathbb{Z}_3$-graded identities of the pair $(M_3(K),gl_3(K))$
论文作者
论文摘要
令$ m_n（k）$为无限积分域$ k $上的$ n \ times n $矩阵的代数。令$ gl_n（k）$为$ n \ times n $矩阵的Lie代数，其通常是$ k $的lie产品。令$ g = \ {g_1，\ ldots，g_n \} $为一组订单$ n $。我们描述了构成对$ g $ $ g $ grad $（m_n（k），gl_n（k））$的多项式，其中由$ n $ -tuple $（g_1，\ ldots，g_n）$引起的基本$ g $ - 级。最后，我们描述了$ \ mathbb {z} _3 $ raded $（m_3（k），gl_3（k））$的明确基础。
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 $(M_3(K),gl_3(K))$.
