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On triple homomorphisms of Lie algebras
OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/6cb97c68-ee92-419f-bc6d-4284b6231ae2 • DOI: https://doi.org/10.1142/S0219498823501682
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.
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.