Generalized conformal derivations of Lie conformal algebras

Let R be a finite Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra CDer(R), the conformal quasiderivation algebra QDer(R) and the generalized conformal derivation algebra GDer(R). The generalized conformal derivation algebra is a natural generalization of the conformal derivation algebra. Obviously, we have the following tower CDer(R) subset of QDer(R) subset of GDer(R) subset of gc(R), where gc(R) is the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal (alpha, beta, gamma)-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal (alpha, beta, gamma)-derivations. In addition, all conformal (alpha, beta, gamma)-derivations of finite simple Lie conformal algebras are characterized.