A classification of polynomial functions satisfying the Jacobi identity over integral domains

被引：0

作者：

Marichal, Jean-Luc ^{[1
]}

Mathonet, Pierre ^{[2
]}

机构：

[1] Univ Luxembourg, Math Res Unit, 6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg

[2] Univ Liege, Dept Math, Allee Decouverte 12-B37, B-4000 Liege, Belgium

来源：

AEQUATIONES MATHEMATICAE | 2017年 / 91卷 / 04期

关键词：

Jacobi's identity; Polynomial; Integral domain;

D O I：

10.1007/s00010-017-0477-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that satisfy the Jacobi identity over infinite integral domains. Although this description depends on the characteristic of the domain, it turns out that all these polynomials are of degree at most one in each indeterminate.

引用

页码：601 / 618

页数：18

共 12 条

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