Related papers: local derivations on Witt algebras

The Virasoro Lie algebra is a one-dimensional central extension of the Witt algebra, which can be realized as the Lie algebra of derivations on the algebra $\cc [t^{\pm}]$ of Laurent polynomials. Using this fact, we define a natural family…

In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra $HO$ over a field of prime characteristic. We first give the generator set of $HO_{\bar{0}}.$ Then we determine the…

Let $\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\in {\mathcal{A}}$ is an all-derivable point of ${\mathcal{A}}$ if every derivable linear mapping $\phi$ at $G$ (i.e. $\phi(ST)=\phi(S)T+S\phi(T)$ for any…

Let $\Omega$ be a compact Hausdorff space and let $A$ be a C$^*$-algebra. We prove that if every weak-2-local derivation on $A$ is a linear derivation and every derivation on $C(\Omega,A)$ is inner, then every weak-2-local derivation…

Let $\theta$ be an isomorphism on $L_0^{\infty} (w)^*$. In this paper, we investigate $\theta$-generalized derivations on $L_0^{\infty} (w)^*$. We show that every $\theta$-centralizing $\theta$-generalized derivation on $L_0^{\infty} (w)^*$…

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…

It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any field of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if…

In the present paper it is proved that every inner 2-local derivation on the matrix ring $M_n(\Re)$ of $n\times n$ matrices over a commutative associative ring $\Re$ is an inner derivation. Also, it is proved that, every derivation on an…

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras…

R.V. Kadison defined the notion of local derivation on an algebra and proved that every continuous local derivation on a von Neumann algebra is a derivation (Kadison 1990). We provide the analogous result in the setting of Jordan triples.

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…

We prove that a von Neumann algebra $M$ is abelian if and only if the square of every derivation on the algebra $S(M)$ of measurable operators, affiliated with $M$, is a local derivation. We also show that for general associative unital…

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…

It is shown that the $W_{1+\infty}$ algebra is nothing but the simplest subalgebra of a $q$-discretized \vi\ algebra, in the language of the KP hierarchy explicitly.

We prove that every derivation acting on a von Neumann algebra $\mathcal{M}$ with values in a quasi-normed bimodule of locally measurable operators affiliated with $\mathcal{M}$ is necessarily inner.

In this article, we introduce the concepts of higher {g_n, h_n}-derivation and Jordan higher {g_n, h_n}-derivation, and then we give a characterization of higher {g_n, h_n}-derivations in terms of {g, h}-derivations. Using this result, we…

This paper is devoted to local derivations on subalgebras on the algebra $S(M, \tau)$ of all $\tau$-measurable operators affiliated with a von Neumann algebra $M$ without abelian summands and with a faithful normal semi-finite trace $\tau.$…

Let ${\mathcal N}$ be the Lie algebra of all $n\times n$ strictly block upper triangular matrices over a field ${\mathbb F}$ relative to a given partition. In this paper, we give an explicit description of all derivations of ${\mathcal N}$.

In this article, we study the derivations of group algebras of some important groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral ($SD_{8n}$). First, we explicitly classify all inner derivations of a group algebra…

We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an…