Related papers: Local derivations on the Lie algebra $W(2,2)$

We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient…

We prove that every 2-local derivation from the algebra $M_n(\mathcal{A})(n>2)$ into its bimodule $M_n(\mathcal{M})$ is a derivation, where $\mathcal{A}$ is a unital Banach algebra and $\mathcal{M}$ is a unital $\mathcal{A}$-bimodule such…

It is proved that every 2-local derivation on an AW$^*$-algebra of type I is a derivation. Also an analog of Gleason theorem for signed measures on projections of homogenous AW$^*$-algebras except the cases of an AW$^*$-algebra of type…

This paper generalizes the concepts of 2-local derivations and biderivations (without the skewsymmetric condition) of a finite-dimensional Lie algebra from the adjoint module to any finite-dimensional module, and determines all 2-local…

The paper is devoted to the description of $2$-local derivations on von Neumann algebras. Earlier it was proved that every $2$-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of…

We prove that every local derivation on a complex semisimple finite-dimensional Leibniz algebra is a derivation.

In this paper, the derivation algebras and automorphism groups of a class of deformative super $W$-algebras $W_{\lambda}(2,2)$ are determined.

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…

Let $L$ be a locally compact Hausdorff space. Suppose $A$ is a C$^*$-algebra with the property that every weak-2-local derivation on $A$ is a {\rm(}linear{\rm)} derivation. We prove that every weak-2-local derivation on $C_0(L,A)$ is a…

We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…

The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove…

This paper is devoted to the study of local and 2-local derivations of nullfiliform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not…

In the present paper we prove that every 2-local derivation on a von Neumann algebra of type I is a derivation.

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra $L^\omega(M, \tau)$ associated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $\tau.$ We prove that every 2-local…

In the present paper, we prove that a local derivation on the octonion (Cayley) algebra $\mathbb{O}$ over an arbitrary field, satisfying some conditions is a derivation, and every 2-local derivation on $\mathbb{O}$ is a Jordan derivation.

For $a,b\in \mathbb{C}$, the Lie algebra $\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\mathcal{W}(a,b)$ are determined. Surprisingly, these…

The present paper is devoted to studying 2-local derivations on the planar Galilean conformal algebra. We prove that every 2-local derivation on the planar Galilean conformal algebra is a derivation.

In this work, we introduce the notion of local and $2$-local $\delta$-derivations and describe local and $2$-local $\frac{1}{2}$-derivation of finite-dimensional solvable Lie algebras with filiform, Heisenberg, and abelian nilradicals.…

The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz…

In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.