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

IF 0.6 4区数学 Q3 MATHEMATICS

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

Artem A. Lopatin, Ronaldo José Sousa Ferreira

引用次数: 1

Abstract

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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若干矩阵的O(3)-不变量的最小生成集与分离集

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:

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operators and Matrices 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： ''Operators and Matrices'' (''OaM'') aims towards developing a high standard international journal which will publish top quality research and expository papers in matrix and operator theory and their applications. The journal will publish mainly pure mathematics, but occasionally papers of a more applied nature could be accepted. ''OaM'' will also publish relevant book reviews. ''OaM'' is published quarterly, in March, June, September and December.