Article (Scientific journals)
A classification of polynomial functions satisfying the Jacobi identity over integral domains
Marichal, Jean-Luc; Mathonet, Pierre
2017In Aequationes Mathematicae, 91 (4), p. 601-618
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Keywords :
Jacobi's identity; polynomial; integral domain
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre;  University of Liège, Belgium > Department of Mathematics
External co-authors :
yes
Language :
English
Title :
A classification of polynomial functions satisfying the Jacobi identity over integral domains
Publication date :
August 2017
Journal title :
Aequationes Mathematicae
ISSN :
1420-8903
Publisher :
Springer, Basel, Switzerland
Volume :
91
Issue :
4
Pages :
601-618
Peer reviewed :
Peer Reviewed verified by ORBi
Name of the research project :
R-AGR-0500 - IRP15 - MRO3 (20150301-20181231) - MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 17 March 2017

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