Generalized derivations of Lie triple systems

Abstract

Abstract In this paper, we present some basic properties concerning the derivation algebra Der ( T ), the quasiderivation algebra QDer ( T ) and the generalized derivation algebra GDer ( T ) of a Lie triple system T , with the relationship Der ( T ) ⊆ QDer ( T ) ⊆ GDer ( T ) ⊆ End ( T ). Furthermore, we completely determine those Lie triple systems T with condition QDer ( T ) = End ( T ). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.