The central part of calculus on manifolds is usually the calculus of differential forms and the best known operators are exterior derivative, Lie derivatives, pullback and insertion operators. Differential forms are a graded commutative algebra and one may ask for the space of graded derivations of it. It was described by Frölicher and Nijenhuis in [1], who found that any such derivation is the...

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using linear methods in \cite{CZZ} and a key construction for we prove that every derivation $W(2, 2)$ derivation. As an application, determine all deformed $\mathfrak{bms}_3$ algebra.

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2 : n;ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2 : n;ω2) with a Block algebra. W...

We introduce Lie-Nijenhuis bialgebroids as Lie endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis groupoids, and key examples include manifolds, holomorphic flat bialgebra bundles. To achieve our goal we develop theory "generalized derivations" their duality, extending the well-established derivations on vector