This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M , of its Lie subalgebra D 1 (M) of all linear first-order differential operators of M , and of the Poisson algebra S(M) = P ol(T * M) of all polynomial functions on T * M, the symbols of the operators in D(M). It turns out that, in terms ...

Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geo...

Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal do not have non-trivial $\frac{1}{2}$-derivations as it follows they admit transposed structures. Also, we proved each finite-dimensional solvable algebra admits a structure ${\rm Hom}$-Lie structure.

Abstract. In this paper we investigate Lie bialgebra structures on a twisted Schrödinger-Virasoro type algebra L. All Lie bialgebra structures on L are triangular coboundary, which is different from the relative result on the original Schrödinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to L⊗L and we develop ...