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Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras
In this paper, we study triple derivations and triple homomorphisms of
perfect Lie superalgebras over a commutative ring . It is proved that, if
the base ring contains , is a perfect Lie superalgebra with
zero center, then every triple derivation of is a derivation, and every
triple derivation of the derivation algebra is an inner derivation.
Let be Lie superalgebras over a commutative ring , the notion of
triple homomorphism from to is introduced. We proved that, under
certain assumptions, homomorphisms, anti-homomorphisms, and sums of
homomorphisms and anti-homomorphisms are all triple homomorphisms.Comment: 12pages in Indagationes Mathematicae, 201
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