Generalized Derivations Of δ-Lie Supertriple Systems And δ- Lie Superalgebras

In this thesis, we mainly study generalized derivations of δ-Lie triple systems, Lie supertriple systems and Jordan Lie superalgebras, respectively. We firstly study some important properties concerning the derivation algebra, the quasiderivation algebra, the generalized derivation algebra, centroids, central derivations of δ-Lie triple systems, as well as obtain a necessary condition for decomposable 6-Lie triple systems. Furthermore, we show that the quasiderivations of a δ-Lie triple system T can be embedded as derivations in a larger δ-Lie triple system. In particular, when the center of T is zero, we have Der(?)=φ(QDer(T))+ZDer(?).We then study certain structural results concerning centroids of Lie supertriple systems. Centroids of the tensor product of a Lie supertriple system and a unital commutative associative algebra are studied. Furthermore, the centroid of a tensor product of a simple Lie supertriple system and a polynomial ring is partly deter-mined. Finally, the concepts of (generalized) (θ,φ)-prederivations and (generalized) Jordan (θ, φ)-prederivations on a δ-Lie superalgebra are introduced. It is proved that Jordan(θ, φ)-prederivations (resp. generalized Jordan (θ, φ)-prederivations) are (θ, φ)-prederivations (resp. generalized (θ, φ)-prederivations) on a δ-Lie su-peralgebra under some conditions. In particular, Jordan θ-prederivations are θ-prederivations on a δ-Lie superalgebra.