Abstract. Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson alge...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In 1935, G. I. Taylor invoked rotational symmetry to derive a remarkable formula for the turbulent dissipation rate. That derivation, though ingenious, leaves it unclear if truly conforms with symmetry. We use machinery of Lie groups furnish rigorous derivation Taylor's under and also not considered by Taylor, reflectional

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.