复正交李超代数osp(1,2)的拟型心与型心的矩阵表示

Matrix Representation of Centroids and Quasi Centroids of the Complex Orthogonal Lie Superalgebras

摘要: 本文为研究复数域上不超过三阶的正交李超代数osp(1,2)的拟型心与型心，应用解线性方程组的方法，分别在奇变换和偶变换两种情况下确定了这些李超代数拟型心和型心的矩阵表示。最终得到其在奇变换下的拟型心在标准基上的矩阵为0_5×5，型心在标准基上的矩阵为0_5×5；其在偶变换下的拟型心在标准基上的矩阵为cI_5×5，型心在标准基上的矩阵为cI_5×5。

Abstract: In this paper, in order to study the centroids and quasi-centroids of the orthogonal Lie superalgebras osp(1,2) over complex fields, the matrix representations of centroid and quasi centroid of osp(1,2) are determined by applying the method of solving the system of linear equa-tions in the cases of odd and even transformations, respectively. The final matrix of its qua-si-centroids on the standard basis under odd transformation is 0_5×5 and the matrix of the cen-troids on the standard basis is 0_5×5; the matrix of its quasi-centroids on the standard basis under even transformation is cI_5×5 and the matrix of the centroids on the standard basis is cI_5×5.