1905年,I.Schur提出特征零代数闭域上的一般线性李代数gLm(F)的交换子代数的最大维数,进而可以确定任一有限维交换的李代数的忠实表示的最小维数.然而,特征为0的代数闭域上的有限维交换李超代数的极小忠实表示仍是一个公开的问题.基于两两交换的矩阵可以同时上三角的事实,利用矩阵的相似变换,确定特征0代数闭域上一般线性李超代数gl(1,n)的不可分解的交换子代数的最大维数.“,”In 1905, I. Schur posed the maximal dimension for abelian subalgebras of the generally linear Lie algebra gLm(F) over algebraically closed fields of characteristic zero. Consequently, it was verified that the minimal faithful representation of any finite dimensional abelian Lie algebra. However, the minimal representation is still open for any finite dimensional abelian Lie superalgebra. By utilizing similar operations for matrices and the fact that mutually commutative matrices are simultaneously upper triangulable, the maximal dimension for any indecom- posable abelian subalgebra of gl( 1 ,n) is computed.