相关论文: Generalized derivations of $3$-Lie algebras

In this paper, we give some basic properties of the generalized derivation algebra ${\rm GDer}(L)$ of a Hom-Lie superalgebra $L$. In particular, we prove that ${\rm GDer}(L) = {\rm QDer}(L) + {\rm QC}(L)$, the sum of the quasiderivation…

In this paper, we present some basic properties concerning the derivation algebra ${\rm Der}(T)$, the quasiderivation algebra ${\rm QDer}(T)$ and the generalized derivation algebra ${\rm GDer}(T)$ of a Lie triple system $T$, with the…

~Let $(g,~[-,-],~\omega)$ be a finite-dimensional complex $\omega$-Lie superalgebra. This paper explores the algbaraic structures of generalized derivation superalgebra ${\rm GDer}(g)$, compatatible generalized derivations algebra ${\rm…

In this paper, we give some properties of generalized derivation algebras of Hom-Jordan algebras. In particular, we show that $GDer(V) = QDer(V) + QC(V)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that…

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…

In this paper, we give some construction about ternary Jordan algebras at first. Next we study relationships between generalized derivations, quasiderivations and centroids of ternary Jordan algebras. We show that for ternary Jordan…

It is well known that n-Hom Lie superalgebras are certain generalizations of n-Lie algebras. This paper is devoted to investigate the generalized derivations of multiplicative n-Hom Lie superalgebras. We generalize the main results of Leger…

This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…

In this paper, we present some basic properties concerning the quasi-derivation algebra $QDer(\mathcal{A})$ and the quasi-centroid algebra $QC(\mathcal{A})$ of associative algebra $\mathcal{A}$. Furthermore, using the result on…

We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color $n$-ary $\Omega$-algebras. Particularly, we prove some properties of generalized derivations of color $n$-ary algebras; prove…

The principal objective of this paper is to determine the structure of $n$-Lie derivations ($n\geq 3$) on generalized matrix algebras.It is shown that under certain mild assumptions, every $n$-Lie derivation can be decomposed into the sum…

The main goal of this paper is to introduce the notion of $3$-L-dendriform algebras which are the dendriform version of $3$-pre-Lie algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of $3$-pre-Lie…

We defined generalized \delta-derivations of algebra A as linear mapping \chi associated with usual \delta-derivation \phi by the rule \chi(xy)=\delta(\chi(x)y+x\phi(y))=\delta(\phi(x)y+x\chi(y)) for any x,y \in A. We described generalized…

Let $\mathcal{R}$ be a finite Lie conformal algebra. In this paper, we first investigate the conformal derivation algebra $CDer(\mathcal{R})$, the conformal triple derivation algebra $CTDer(\mathcal{R})$ and the generalized conformal triple…

Let $\mathcal{R}$ be a Lie conformal superalgebra. In this paper, we first investigate the conformal derivation algebra $CDer(\mathcal{R})$, the conformal triple derivation algebra $CTDer(\mathcal{R})$, and the generalized conformal triple…

In this paper, we introduce the notion of generalized representation of a $3$-Lie algebra, by which we obtain a generalized semidirect product $3$-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of…

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition…

We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…

Let $\Gamma$ be a generic subgroup of the multiplicative group $\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $\Gamma$, called twisted $\Gamma$-Lie algebras, which is a natural generalization of…

Let $A$ be a Banach algebra and $M$ be a Banach right $A$-module. A linear map $\delta : M\to M$ is called a generalized derivation if there exists a derivation $d : A \to A$ such that $$\delta(xa)=\delta(x)a + x d(a) \quad (a \in A, x \in…