Related papers: Local derivation on the $n$-th Schr{\"o}dinger alg…

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 aim of this article is to discuss the $n$-derivation algebras of Lie color algebras. It is proved that, if the base ring contains $\frac{1}{n-1}$, $L$ is a perfect Lie color algebra with zero center, then every triple derivation of $L$…

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 $A$ be a C$^*$-algebra, and let $X$ be a Banach $A$-bimodule. B. E. Johnson showed that local derivations from $A$ into $X$ are derivations. We extend this concept of locality to the higher cohomology of a $C^*$-algebra %for…

It is shown that the cubic derivative nonlinear Schr\"odinger equation is locally well-posed in Besov spaces $B^{s}_{2,\infty}(\mathbb X)$, $s\ge\tfrac12$, where we treat the non-periodic setting $\mathbb X=\mathbb R$ and the periodic…

We consider the derivative nonlinear Schr\"odinger equation on the real line, with a background function $\psi(t,x)\in L^\infty(\mathbb{R}^2)$ that satisfies suitable conditions. Such a function may, for example, be a non-decaying solution…

In this paper, we prove that every invertible $2$-local or local automorphism of a simple generalized Witt algebra over any field of characteristic $0$ is an automorphism. In particular, every $2$-local or local automorphism of Witt…

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…

In this paper, we construct for every $\alpha >0$ and $\lambda \in {\mathbb C}$ a space of initial values for which there exists a local solution of the nonlinear Schr\"odinger equation \begin{equation*} \begin{cases} iu_t + \Delta u +…

In this work, we describe local and 2-local $\frac12$-derivations of infinite-dimensional Lie algebras. We prove that all local and 2-local $\frac12$-derivations of the Witt algebra as well as of the positive Witt algebra and the classical…

Let $\mathcal{A}$ be a unital associative algebra and $\mathcal{M}$ be an $\mathcal{A}$-bimodule. A linear mapping $\varphi$ from $\mathcal{A}$ into an $\mathcal{A}$-bimodule $\mathcal{M}$ is called a Lie derivation if…

The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency $3$ and $4$ admit local derivation (local automorphisms) which is…

Given a von Neumann algebra $M$ we introduce so called central extension $mix(M)$ of $M$. We show that $mix(M)$ is a *-subalgebra in the algebra $LS(M)$ of all locally measurable operators with respect to $M,$ and this algebra coincides…

To each projection $p$ in a $C^*$-algebra $A$ we associate a family of derivations on $A$, called $p$-derivations, and relate them to the space of triple derivations on $p A (1-p)$. We then show that every derivation on a ternary ring of…

We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We…

The aim of this paper is to describe all inner and all outer derivations of Leavitt path algebra W(n) via explicit formulas. In fact the space of all inner and all outer derivations of the Leavitt path algebra W(n) has been described.

In this paper, the generalized Loop Heisenberg-Virasoro algebra is introduced. Firstly, we determine the derivations on the generalized Loop Heisenberg-Virasoro algebra. Then we show that all 2-local derivations are derivations.…

Given a von Neumann algebra $M$ denote by $S(M)$ and $LS(M)$ respectively the algebras of all measurable and locally measurable operators affiliated with $M.$ For a faithful normal semi-finite trace $\tau$ on $M$ let $S(M, \tau)$ (resp.…

We prove that, for every separable complex Hilbert space $H$, every weak-2-local $^*$-derivation on $B(H)$ is a linear $^*$-derivation. We also establish that every (non-necessarily linear nor continuous) weak-2-local derivation on a finite…

The present paper is devoted to study 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra. We prove that all 2-local superderivations on the super Virasoro algebra as well as the super W(2,2) algebra are…