Jordan Gn-derivations on path algebras
Commun. Korean Math. Soc.
Published online May 13, 2022
Abderrahim Adrabi, Driss Bennis, and Brahim Fahid
Faculty of Sciences, Mohammed V University in Rabat, Morocco; Faculty of Sciences, Mohammed V University in Rabat, Morocco; Superior School of Technology, Ibn Tofail University, Kenitra, Morocco
Abstract : In this paper, we introduce the notion of Jordan Gn-derivations, with n ≥ 2, which is a natural generalization of Bresar’s Jordan {g,h}-derivations. In order to answer some natural questions on it, we focus our study on its form on
path algebras. We prove that, when n > 2, every Jordan Gn-derivation on a path algebra is a {g,h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky
conjecture on path algebras. Namely, we show that the set of values of a multilinear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length great or equals to one.
Keywords : Path Algebras; Derivations; Jordan Gn-derivations; Jordan {g,h}-derivations; Lvov-Kaplansky conjecture
MSC numbers : 15A78, 16S10, 16W10, 16W25
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