2-Local derivations on algebras of locally measurable operators

The paper is devoted to 2-local derivations on the algebra $LS(M)$ of all locally measurable operators affiliated with a type I$_\infty$ von Neumann algebra $M.$ We prove that every 2-local derivation on $LS(M)$ is a derivation.Comment: arXiv admin note: substantial text overlap with arXiv:1110.155

n-Dimensional filiform Leibniz algebras of length (n-1) and their derivations

In this work $n$-dimensional filiform Leibniz algebras admitting a gradation of length $(n-1)$ are classified. Derivations of such algebras are also described.Comment: 15 page