论文标题
对尼尔植物运算符的对成对的内核和矩阵的一维交集与Weyr矩阵通勤
Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix
论文作者
论文摘要
I.M. Gelfand和V.A. Ponomarev（1969）证明，对向量空间上的nilpotent运算符进行对nilpotent运算符进行分类的问题包含了对任意的线性运算符的任意t键盘进行分类的问题。此外，它包含分类任意颤抖的表示的问题，因此被认为是绝望的。如果A和B的核的相交是一维的，则我们给出（a，b）的矩阵的简单正常形式。我们证明，如果A的Jordan矩阵是相同大小的Jordan块的直接总和，并且该场的特征为零，则该形式是规范的。
I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an arbitrary t-tuple of linear operators. Moreover, it contains the problem of classifying representations of an arbitrary quiver, and so it is considered as hopeless. We give a simple normal form of the matrices of (A,B) if the intersection of kernels of A and B is one-dimensional. We prove that this form is canonical if the Jordan matrix of A is a direct sum of Jordan blocks of the same size and the field is of zero characteristic.
