[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 :
Mathématiques
Auteur, co-auteur :
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
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
A classification of polynomial functions satisfying the Jacobi identity over integral domains
