论文标题
上三角基质代数上多线性分级多项式的图像
Images of multilinear graded polynomials on upper triangular matrix algebras
论文作者
论文摘要
在本文中，我们研究了上三角矩阵UT_N的分级代数上多线分级多项式的图像。对于正整数q \ leq n，我们将这些图像分类为ut_n，并具有特定的基本ZQ-grading。结果，我们获得了自然z_n分级的UT_N上多线性分级多项式的图像。我们应用此分类，以便根据分级身份为多连线多项式提供新的条件，以便在完整矩阵代数上获得其图像中的无纹状矩阵。我们还描述了分级代数UT_2和UT_3上的多线性多项式的图像，以进行任意等级。我们通过证明分级的Jordan代数UJ_2的结果以及对自然基本Z_3毕业生的UJ_3的结果来完成纸张。
In this paper we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices UT_n. For positive integers q \leq n, we classify these images on UT_n endowed with a particular elementary Z_q-grading. As a consequence, we obtain the images of multilinear graded polynomials on UT_n with the natural Z_n-grading. We apply this classification in order to give a new condition for a multilinear polynomial in terms of graded identities so that to obtain the traceless matrices in its image on the full matrix algebra. We also describe the images of multilinear polynomials on the graded algebras UT_2 and UT_3, for arbitrary gradings. We finish the paper by proving a similar result for the graded Jordan algebra UJ_2, and also for UJ_3 endowed with the natural elementary Z_3-grading.
