alexa Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras


Journal of Generalized Lie Theory and Applications

Author(s): Jia Zhou, Liangyun Chen

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In this paper, we study triple derivations and triple homomorphisms of perfect Liesuperalgebras over a commutative ringR. It is proved that, if the base ring contains12,Lisa perfect Lie superalgebra with zero center, then every triple derivation ofLis a derivation,and every triple derivation of the derivation algebraDer(L) is an inner derivation. LetL, L′be Lie superalgebras over a commutative ringR, the notion of triple homomorphismfromLtoL′is introduced. We proved that, under certain assumptions, homomorphisms,anti-homomorphisms, and sums of homomorphisms and anti-homomorphisms are all triplehomomorphisms.


This article was published in Comm. Algebras 41: 1647-1654 and referenced in Journal of Generalized Lie Theory and Applications

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