Author(s): Jia Zhou, Liangyun Chen
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.