On triple homomorphisms of Lie algebras

Mohammad Jafari , Ali Reza Madadi, Gunnar Traustason

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Abstract

Let L and K be two Lie algebras over a commutative ring with identity. In this paper, under some conditions on L and K, it is proved that every triple homomorphism from L onto K is the sum of a homomorphism and an antihomomorphism from L
into K. We also show that a finite-dimensional Lie algebra L over an algebraically closed field of characteristic zero is nilpotent of class at most 2 if and only if the sum of every homomorphism and every antihomomorphism on L is a triple homomorphism.
Original languageEnglish
Article number2350168
JournalJournal of Algebra and its Applications
Volume22
Issue number8
DOIs
Publication statusPublished - 12 May 2022

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