Simultaneous direct sum decompositions of several multivariate polynomials

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-02 DOI:10.1016/j.laa.2025.06.022

Lishan Fang, Hua-Lin Huang, Lili Liao

引用次数: 0

Abstract

We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method.

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几个多元多项式的同时直接和分解

研究多元多项式集的同时直接和分解问题。为此，我们将哈里森的单一齐次多项式中心理论推广到更广泛的情况下。证明了多项式集的中心是一个特殊的约当代数，并证明了给定多项式的同时直接和分解与中心代数的正交幂等的完备集是双射的。给出了几个例子来说明该方法的性能。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.