Semi-invariants of quivers as determinants
Semi-invariants of quivers as determinants
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作为行列式的箭袋半不变量
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Zubkov
中科院分区：
文献类型：
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作者：
M. Domokos;A. Zubkov
箭图的表示由一组矩阵给出。箭图的半不变量可以通过将包含表示的矩阵分量和单位矩阵的行列式的允许部分极化作为块来构造。我们证明了对于任意箭图和任意无限基场，这些行列式半不变量横跨所有半不变量空间。在证明过程中，我们证明了可以将生成半不变量的研究简化到箭图没有长度大于1的有向路径的情况。
A representation of a quiver is given by a collection of matrices. Semi-invariants of quivers can be constructed by taking admissible partial polarizations of the determinant of matrices containing sums of matrix components of the representation and the identity matrix as blocks. We prove that these determinantal semi-invariants span the space of all semi-invariants for any quiver and any infinite base field. In the course of the proof we show that one can reduce the study of generating semi-invariants to the case when the quiver has no oriented paths of length greater than one.