Generalized conformal derivations of Lie conformal algebras

Abstract

Let $R$ be a 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 $CDer(R)\subseteq QDer(R)\subseteq GDer(R)\subseteq gc(R)$, 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.

17pages

References in corpus (2)

• On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functions
• Loop Virasoro Lie Conformal Algebra

Cited by in corpus (1)

• Deformations and generalized derivations of Lie conformal superalgebras