若干矩阵的O(3)-不变量的最小生成集与分离集

Pub Date : 2023-01-01 DOI:10.7153/oam-2023-17-42

Artem A. Lopatin, Ronaldo José Sousa Ferreira

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引用次数: 1

摘要

给定向量空间$H$上的群$G$作用的多项式不变量的代数$F[H]^G$，如果$S$分离了所有可以被$F[H]^G$分离的轨道，则$F[H]^G$的子集$S$被称为分离。在正交群的情况下，对任意特征不同于两个的无限域上若干矩阵的矩阵不变量的代数，找到了一个极小分离集。即，我们考虑以下情况:

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Minimal generating and separating sets for O(3)-invariants of several matrices

Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating set is found for some algebras of matrix invariants of several matrices over an infinite field of arbitrary characteristic different from two in case of the orthogonal group. Namely, we consider the following cases:

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