We study the differential polynomial identities of the algebra UT_m(F) under the derivation action of the two dimensional metabelian Lie algebra, obtaining a generating set of the T_L-ideal they constitute. Then we determine the S_n-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence.

中文翻译：

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二维Metabelian李代数作用下上三角矩阵的多项式恒等式

我们研究了二维Metabelian Lie代数的推导作用下代数U T _m（F）的微分多项式恒等式，从而获得了它们构成的T _L-理想的生成集。然后，我们确定其适当的多线性空间的S _n结构，并在最小情况下m = 2、3时确定其精确的微分维数序列。