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 toweris the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal (α, β , γ)-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal (α, β , γ)-derivations. In addition, all conformal (α, β , γ)-derivations of finite simple Lie conformal algebras are characterized.In this section, for the reader's convenience, we shall summarize some basic facts about Lie conformal algebras used in this paper, see [4,8,9]. Definition 2.1. A Lie conformal algebra R is an A -module endowed with a C-bilinear map

Deformations and generalized derivations of Hom-Lie conformal algebras

“…In [6,9], we studied Hom-Nijienhuis operators and T *-extensions of Hom-Lie superalgebras and Hom-Jordan Lie algebras, extending the generalized derivation theory of Lie algebras given in [5]. Recently, similar researches were done for Lie conformal algebras in [4]. In the present paper, we aim to study generalized derivations of Hom-Lie conformal algebras, and extend the cohomology theory of Lie conformal algebras to the Hom case.…”

Representations of Some Associative Pseudoalgebras

“…After this, Y. Su determined the cohomology groups of a general linear conformal Lie algebra in [Su]. Further, Su and his coauthors study representations of various conformal Lie algebras (see [FHS,HS1,HS2,SY,SY1,SY2]).…”

Conformal $(\si,\t)$-Derivations on Lie conformal superalgebras

“…The derivation theory of Lie conformal (super)algebras was introduced in [2,3]. Lately, the generalized derivation theory of Lie conformal (super)algebras was developed in [4,9,10]. [8,11] studied the (α, β, γ)-derivations of Lie (super)algebras.…”

“…[1] studied a kind of new generalized derivations of Lie algebras, that is the (σ, τ)-derivation theory of Lie algebras. In the present paper, we aim to do same in [1,4] for Lie conformal superalgebras, extend the (σ, τ)-derivations of Lie algebras and conformal (α, β, γ)-derivations of Lie conformal algebras to the Lie conformal superalgebras.…”